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➡️ Part 31 of Quantitative Finance From Scratch: implied volatility. The Black-Scholes formula from part 30 needs five inputs. Four of them you can look up (stock price, strike, rate and time), but the fifth, the volatility over the life of the option, lies in the future. Traders form...

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QuantFinanceToGo

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51,900 просмотров • 21 дней назад •via TikTok

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➡️ Part 30 of Quantitative Finance From Scratch: the Black-Scholes formula. A call option is the right to buy a stock at a fixed price (the strike) on a fixed date. Fischer Black and Myron Scholes published the formula in 1973 (Journal of Political Economy), Robert Merton derived it another way, and in 1997 Scholes and Merton received the Nobel Memorial Prize in Economic Sciences. Black had died in 1995. C = S N(d1) - K e^(-rt) N(d2), with d1 = [ln(S/K) + (r + σ²/2) t] / (σ √t) and d2 = d1 - σ √t. S is today's stock price, K the strike, r the risk free rate, t the time to expiry in years, σ the volatility, and N the cumulative standard normal distribution. The stock's expected return does not appear, because stock and cash can copy the option. Our test run (blackscholes.py, 16 lines of numpy, seed 30): stock 100, strike 100, 1 year, rate 4 %, volatility 20 %. Then d1 = 0.3, d2 = 0.1, N(d1) = 0.618, N(d2) = 0.540, and the price is 61.79 - 51.87 = 9.93. One million risk neutral Monte Carlo prices give an average discounted payoff of 9.92 (standard error 0.014). With the stock at 100 the same option costs 4.49 with 3 months left and 15.08 with 2 years left. Honest notes: the model assumes a constant volatility and price paths without jumps. If you solve the formula backwards from real option prices, the volatility changes with the strike (the smile), so in practice each option gets its own implied volatility for the stock. #quantfinance #blackscholes #options #finance #python
2:30

➡️ Part 30 of Quantitative Finance From Scratch: the Black-Scholes formula. A call option is the right to buy a stock at a fixed price (the strike) on a fixed date. Fischer Black and Myron Scholes published the formula in 1973 (Journal of Political Economy), Robert Merton derived it another way, and in 1997 Scholes and Merton received the Nobel Memorial Prize in Economic Sciences. Black had died in 1995. C = S N(d1) - K e^(-rt) N(d2), with d1 = [ln(S/K) + (r + σ²/2) t] / (σ √t) and d2 = d1 - σ √t. S is today's stock price, K the strike, r the risk free rate, t the time to expiry in years, σ the volatility, and N the cumulative standard normal distribution. The stock's expected return does not appear, because stock and cash can copy the option. Our test run (blackscholes.py, 16 lines of numpy, seed 30): stock 100, strike 100, 1 year, rate 4 %, volatility 20 %. Then d1 = 0.3, d2 = 0.1, N(d1) = 0.618, N(d2) = 0.540, and the price is 61.79 - 51.87 = 9.93. One million risk neutral Monte Carlo prices give an average discounted payoff of 9.92 (standard error 0.014). With the stock at 100 the same option costs 4.49 with 3 months left and 15.08 with 2 years left. Honest notes: the model assumes a constant volatility and price paths without jumps. If you solve the formula backwards from real option prices, the volatility changes with the strike (the smile), so in practice each option gets its own implied volatility for the stock. #quantfinance #blackscholes #options #finance #python

QuantFinanceToGo

24,700 просмотров • 23 дней назад

↕️Deconstructing the implied volatility of options and capturing the gap in market expectations 🔺Based on the option smile curve and Monte Carlo simulation, quantitatively analyze the long-short divergence in the options market, and help investors grasp the volatility dividend
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↕️Deconstructing the implied volatility of options and capturing the gap in market expectations 🔺Based on the option smile curve and Monte Carlo simulation, quantitatively analyze the long-short divergence in the options market, and help investors grasp the volatility dividend

TSAI

22,640 просмотров • 1 год назад

➡️ Quantitative Finance from Scratch, part 35: how market makers make money. The first source is the spread. Like an exchange booth, a market maker buys a little below the fair price at the bid and sells a little above it at the ask, so every trade earns half the gap whatever the stock does next. After selling a call, it buys delta shares, so small moves no longer matter. The second source comes from the other Greeks: theta is the income, because the call it owes loses value every day, and gamma is the cost, because after every big move it must buy shares high and sell them low to keep the hedge. If the stock moves exactly as much as the implied volatility in the price, income and cost cancel. If it stays calmer, the market maker earns, and if it moves more, it loses. Vega is the risk to this income, because a jump in implied volatility makes the call it owes more expensive. If a customer sells it the call instead, everything flips. The code (marketmaker.py, 16 lines) sells our call from part 33 at the ask (fair $10.45, ask $10.55, bid $10.35) and hedges it every day on 2,000 simulated years with an implied volatility of 20 %. With a real volatility of 16 % it earns $1.59 per call on average and every path ends in profit; at 20 % it earns $0.10, about the spread; at 24 % it loses $1.41 and only 0.3 % of paths end in profit. Honest notes: a simplified model with one option, daily hedging, Black Scholes prices, constant volatility, no trading costs, no dividends and no other customers. Real market makers manage many options at once and also face fees, inventory limits and jumps. #quantfinance #options #marketmaking #greeks #finance
2:35

➡️ Quantitative Finance from Scratch, part 35: how market makers make money. The first source is the spread. Like an exchange booth, a market maker buys a little below the fair price at the bid and sells a little above it at the ask, so every trade earns half the gap whatever the stock does next. After selling a call, it buys delta shares, so small moves no longer matter. The second source comes from the other Greeks: theta is the income, because the call it owes loses value every day, and gamma is the cost, because after every big move it must buy shares high and sell them low to keep the hedge. If the stock moves exactly as much as the implied volatility in the price, income and cost cancel. If it stays calmer, the market maker earns, and if it moves more, it loses. Vega is the risk to this income, because a jump in implied volatility makes the call it owes more expensive. If a customer sells it the call instead, everything flips. The code (marketmaker.py, 16 lines) sells our call from part 33 at the ask (fair $10.45, ask $10.55, bid $10.35) and hedges it every day on 2,000 simulated years with an implied volatility of 20 %. With a real volatility of 16 % it earns $1.59 per call on average and every path ends in profit; at 20 % it earns $0.10, about the spread; at 24 % it loses $1.41 and only 0.3 % of paths end in profit. Honest notes: a simplified model with one option, daily hedging, Black Scholes prices, constant volatility, no trading costs, no dividends and no other customers. Real market makers manage many options at once and also face fees, inventory limits and jumps. #quantfinance #options #marketmaking #greeks #finance

QuantFinanceToGo

102,600 просмотров • 15 дней назад

➡️ Part 32 of Quantitative Finance From Scratch: put call parity. A call gives you the right to buy a stock at the strike on a fixed date, and a put gives you the right to sell it at that price. If you buy a call and sell a put with the same strike and the same date, you end up buying the stock at the strike whatever happens, because above the strike you use your call, and below it the buyer of your put sells you the stock. That sure deal is worth the stock price today minus the present value of the strike, so the call minus the put equals the stock minus the present value of the strike. Our test run (putcall.py, 16 lines of plain Python) prices both options with Black Scholes for a stock and a strike of 100 dollars, a rate of 5 %, one year and a volatility of 20 %. The call costs 10.45 dollars and the put 5.57 dollars, and their difference of 4.88 dollars equals 100 minus 95.12, the present value of the strike. Six end prices drawn with seed 32 show that the call minus the put always pays the end price minus the strike. The rule needs no model for the stock price (Merton 1973), so traders use it to check quotes and to turn a call price into a put price. It holds exactly for European options, which can only be used at expiry, on stocks without dividends. #quantfinance #putcallparity #options #blackscholes #python
1:21

➡️ Part 32 of Quantitative Finance From Scratch: put call parity. A call gives you the right to buy a stock at the strike on a fixed date, and a put gives you the right to sell it at that price. If you buy a call and sell a put with the same strike and the same date, you end up buying the stock at the strike whatever happens, because above the strike you use your call, and below it the buyer of your put sells you the stock. That sure deal is worth the stock price today minus the present value of the strike, so the call minus the put equals the stock minus the present value of the strike. Our test run (putcall.py, 16 lines of plain Python) prices both options with Black Scholes for a stock and a strike of 100 dollars, a rate of 5 %, one year and a volatility of 20 %. The call costs 10.45 dollars and the put 5.57 dollars, and their difference of 4.88 dollars equals 100 minus 95.12, the present value of the strike. Six end prices drawn with seed 32 show that the call minus the put always pays the end price minus the strike. The rule needs no model for the stock price (Merton 1973), so traders use it to check quotes and to turn a call price into a put price. It holds exactly for European options, which can only be used at expiry, on stocks without dividends. #quantfinance #putcallparity #options #blackscholes #python

QuantFinanceToGo

23,300 просмотров • 20 дней назад

➡️ Quantitative Finance from Scratch, part 33: delta and delta hedging. Delta is how much the price of an option moves when the stock moves by one dollar. For a call it lies between zero and one, and in Black Scholes it is N(d1), the same term as in the price formula from part 30. In our test run with the stock and the strike at $100, a 5 % rate, one year and 20 % volatility, the call costs $10.45 and has a delta of 0.64, so a $1 rise lifts the call by about 64 cents. Whoever sold the call holds 0.64 shares against it, and for small moves the loss on the call and the gain on the shares cancel out, which is called delta neutral. Because delta changes whenever the stock moves, the shares have to be rebalanced again and again. The code (delta.py, 16 lines, seed 33) also simulates 2,000 years of a stock with daily rebalancing: the hedged result has a spread of $0.44, against $15.39 without the hedge. Honest notes: the model assumes constant volatility, no trading costs and no dividends; real hedging adds costs and jumps the model does not see. Education only, not financial advice. #quantfinance #options #finance #delta #hedging
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➡️ Quantitative Finance from Scratch, part 33: delta and delta hedging. Delta is how much the price of an option moves when the stock moves by one dollar. For a call it lies between zero and one, and in Black Scholes it is N(d1), the same term as in the price formula from part 30. In our test run with the stock and the strike at $100, a 5 % rate, one year and 20 % volatility, the call costs $10.45 and has a delta of 0.64, so a $1 rise lifts the call by about 64 cents. Whoever sold the call holds 0.64 shares against it, and for small moves the loss on the call and the gain on the shares cancel out, which is called delta neutral. Because delta changes whenever the stock moves, the shares have to be rebalanced again and again. The code (delta.py, 16 lines, seed 33) also simulates 2,000 years of a stock with daily rebalancing: the hedged result has a spread of $0.44, against $15.39 without the hedge. Honest notes: the model assumes constant volatility, no trading costs and no dividends; real hedging adds costs and jumps the model does not see. Education only, not financial advice. #quantfinance #options #finance #delta #hedging

QuantFinanceToGo

90,400 просмотров • 19 дней назад

➡️ Quantitative Finance from Scratch, part 41: Volatility Targeting. In quant finance, risk is usually measured as volatility, how strongly a price swings up and down. Volatility comes in clusters, so stormy days tend to follow stormy days, and that makes it possible to forecast it to some extent. GARCH from parts 39 and 40 is one way to do that; rolling averages and exponentially weighted averages are others. Volatility targeting takes that forecast and compares it with a risk target you choose yourself. If your target is 10 % a year and the forecast for the market is 20 %, the market is twice as wild as you want, so you hold 10 / 20 = 50 % of your money in the market, and your risk stays at 10 %. In general: exposure = target volatility / forecast volatility. When the forecast is above your target, you hold less than all of your money. When it is below, the rule asks for more than 100 %, which means borrowing, so the exposure usually gets a cap. One limit remains: every forecast looks back. A sudden crash after a calm stretch still hits a full position, and only afterwards does the forecast jump and the position shrink. The code (vt_reel.py, 15 lines of Python with numpy) is general on purpose: a GARCH forecast for tomorrow from today's move and today's forecast (omega 0.05, alpha 0.10, beta 0.85 in percent squared per day, as in part 39), the rule exposure = target / forecast with a cap, and a daily loop over the returns that sets the exposure before each day and updates the forecast after it. #quantfinance #volatility #riskmanagement #finance #portfoliomanagement Education only, not financial advice.
1:28

➡️ Quantitative Finance from Scratch, part 41: Volatility Targeting. In quant finance, risk is usually measured as volatility, how strongly a price swings up and down. Volatility comes in clusters, so stormy days tend to follow stormy days, and that makes it possible to forecast it to some extent. GARCH from parts 39 and 40 is one way to do that; rolling averages and exponentially weighted averages are others. Volatility targeting takes that forecast and compares it with a risk target you choose yourself. If your target is 10 % a year and the forecast for the market is 20 %, the market is twice as wild as you want, so you hold 10 / 20 = 50 % of your money in the market, and your risk stays at 10 %. In general: exposure = target volatility / forecast volatility. When the forecast is above your target, you hold less than all of your money. When it is below, the rule asks for more than 100 %, which means borrowing, so the exposure usually gets a cap. One limit remains: every forecast looks back. A sudden crash after a calm stretch still hits a full position, and only afterwards does the forecast jump and the position shrink. The code (vt_reel.py, 15 lines of Python with numpy) is general on purpose: a GARCH forecast for tomorrow from today's move and today's forecast (omega 0.05, alpha 0.10, beta 0.85 in percent squared per day, as in part 39), the rule exposure = target / forecast with a cap, and a daily loop over the returns that sets the exposure before each day and updates the forecast after it. #quantfinance #volatility #riskmanagement #finance #portfoliomanagement Education only, not financial advice.

QuantFinanceToGo

10,300 просмотров • 10 дней назад

➡️ Quantitative Finance from Scratch, part 37: Binomial model option pricing The stock moves in steps, and each step goes up or down by a fixed factor that comes from the volatility. In one step of one year, a stock at $100 goes to $122.14 or $81.87, and a call with strike $100 pays $22.14 or nothing. To get one price today, we average the two payoffs with weights that price the stock correctly: on average it must grow like money in the bank at 5 %, which gives 58 % for up and 42 % for down. These weights are the risk neutral probability. They also price the option, because a mix of stock and cash can copy it exactly. 58 % of $22.14, discounted at 5 %, gives $12.16. With many small steps the branches join again, and walking backwards through the tree gives the price, which zigzags toward the Black-Scholes value of $10.45. The code (binomial.py, 16 lines) builds the Cox-Ross-Rubinstein tree for S = K = 100, r = 5 %, volatility 20 %, one year: $12.16 with one step, $9.54 with two, $11.04 with three, $10.25 with ten and $10.45 with 1,000 steps, against Black-Scholes $10.45. With the same numbers, a put is worth $5.57 as a European option and $6.09 as an American option that can be exercised early (1,000 steps). Source: Cox, Ross and Rubinstein, "Option pricing: A simplified approach", Journal of Financial Economics, 1979. Honest notes: the model assumes a constant volatility and interest rate, no fees and trading at every step; real prices do not move in fixed steps. #quantfinance #options #trading #blackscholes #finance Education only, not financial advice.
1:58

➡️ Quantitative Finance from Scratch, part 37: Binomial model option pricing The stock moves in steps, and each step goes up or down by a fixed factor that comes from the volatility. In one step of one year, a stock at $100 goes to $122.14 or $81.87, and a call with strike $100 pays $22.14 or nothing. To get one price today, we average the two payoffs with weights that price the stock correctly: on average it must grow like money in the bank at 5 %, which gives 58 % for up and 42 % for down. These weights are the risk neutral probability. They also price the option, because a mix of stock and cash can copy it exactly. 58 % of $22.14, discounted at 5 %, gives $12.16. With many small steps the branches join again, and walking backwards through the tree gives the price, which zigzags toward the Black-Scholes value of $10.45. The code (binomial.py, 16 lines) builds the Cox-Ross-Rubinstein tree for S = K = 100, r = 5 %, volatility 20 %, one year: $12.16 with one step, $9.54 with two, $11.04 with three, $10.25 with ten and $10.45 with 1,000 steps, against Black-Scholes $10.45. With the same numbers, a put is worth $5.57 as a European option and $6.09 as an American option that can be exercised early (1,000 steps). Source: Cox, Ross and Rubinstein, "Option pricing: A simplified approach", Journal of Financial Economics, 1979. Honest notes: the model assumes a constant volatility and interest rate, no fees and trading at every step; real prices do not move in fixed steps. #quantfinance #options #trading #blackscholes #finance Education only, not financial advice.

QuantFinanceToGo

26,700 просмотров • 13 дней назад

➡️ Quantitative Finance from Scratch, part 48: Inventory Risk. A market maker always quotes a price you can buy at (ask) and a price you can sell at (bid) and earns the gap. Its inventory is the stock it holds right now: when you sell to it, the inventory grows, when you buy from it, the inventory shrinks. In a calm market, buyers and sellers arrive about equally often, so the inventory stays near zero. Orders often come in waves. When many people sell at once, the market maker keeps buying and the shares pile up. Then every move in the price hits the whole position. Example: with 5,000 shares, a drop of 10 cents costs $500, as much as the spread earns on 12,500 shares at 4 cents each (P&L = cash + inventory × fair price). So it fights back with its prices. With too much stock, it lowers both its bid and its ask: the cheaper ask attracts buyers, the lower bid brings in fewer sellers, and the inventory shrinks again. With too little stock, it raises both prices. This is called skewing the quotes. When prices move fast, it also widens the spread, and if the position still grows too large, it hedges it or sells part of it. Avellaneda and Stoikov (2008, Quantitative Finance 8(3)) turned this into a formula, the reservation price r = s − q·γ·σ²·(T − t): s fair price, q inventory, γ risk aversion, σ volatility, T − t time left. The more inventory, risk aversion and volatility, the further the quotes move away from the fair price. The code (inv_reel.py, 15 lines of plain Python without packages) is general on purpose: booking a fill, the profit and loss, a half spread that grows with volatility, and quotes around the reservation price. Part 49 looks at the second risk, trading with someone who knows more. If you want to go deeper, check out the full course I built: quantfinancetogo.com #quantfinance #marketmaking #inventoryrisk #finance #python Education only, not financial advice.
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➡️ Quantitative Finance from Scratch, part 48: Inventory Risk. A market maker always quotes a price you can buy at (ask) and a price you can sell at (bid) and earns the gap. Its inventory is the stock it holds right now: when you sell to it, the inventory grows, when you buy from it, the inventory shrinks. In a calm market, buyers and sellers arrive about equally often, so the inventory stays near zero. Orders often come in waves. When many people sell at once, the market maker keeps buying and the shares pile up. Then every move in the price hits the whole position. Example: with 5,000 shares, a drop of 10 cents costs $500, as much as the spread earns on 12,500 shares at 4 cents each (P&L = cash + inventory × fair price). So it fights back with its prices. With too much stock, it lowers both its bid and its ask: the cheaper ask attracts buyers, the lower bid brings in fewer sellers, and the inventory shrinks again. With too little stock, it raises both prices. This is called skewing the quotes. When prices move fast, it also widens the spread, and if the position still grows too large, it hedges it or sells part of it. Avellaneda and Stoikov (2008, Quantitative Finance 8(3)) turned this into a formula, the reservation price r = s − q·γ·σ²·(T − t): s fair price, q inventory, γ risk aversion, σ volatility, T − t time left. The more inventory, risk aversion and volatility, the further the quotes move away from the fair price. The code (inv_reel.py, 15 lines of plain Python without packages) is general on purpose: booking a fill, the profit and loss, a half spread that grows with volatility, and quotes around the reservation price. Part 49 looks at the second risk, trading with someone who knows more. If you want to go deeper, check out the full course I built: quantfinancetogo.com #quantfinance #marketmaking #inventoryrisk #finance #python Education only, not financial advice.

QuantFinanceToGo

13,600 просмотров • 2 дней назад

➡️ Quantitative Finance from Scratch, part 43: Black-Litterman. Fischer Black and Robert Litterman published it in 1992 as an improvement on the Markowitz optimizer. Markowitz needs each asset's expected return and volatility. Volatility is fairly easy to estimate, expected returns are very hard, and small errors in them push the weights to extremes. Black-Litterman starts from the market portfolio instead: all the money invested in a market, with each asset's weight equal to its share of the total. As in the CAPM part, this portfolio is optimal in equilibrium, so the model works backwards and asks which returns would make it optimal. The answer is π = δΣw: the market weights w, the covariance matrix Σ (how strongly the assets swing and move together) and the risk aversion δ (extra return demanded per unit of risk) give the implied returns π. Example with 60 % stocks and 40 % bonds, assuming 15 % volatility for stocks, 5 % for bonds, a correlation of 0.2 and δ = 2.5: stocks imply about 3.5 % above the risk free rate (3.525 %), bonds 0.475 %. Then you add your own view, for example stocks earn 6 %, and say how sure you are. The model mixes market and view like a weighted average. If you are as sure as the market (view uncertainty Ω = τσ² with τ = 0.05), stocks land at about 4.8 % (4.7625 %), exactly halfway. Without any view you get back the market portfolio. The code (bl_reel.py, 13 lines of plain Python without packages) is general on purpose: implied returns from risk aversion, covariance and weights, how much of your trust goes to your view, and the weighted average of market and view. For a single view on one asset this is exactly the full Black-Litterman formula. Source: Black, F. and Litterman, R. (1992), Global Portfolio Optimization, Financial Analysts Journal 48(5), 28-43. #quantfinance #finance #portfoliooptimization #markowitz #assetallocation Education only, not financial advice.
1:44

➡️ Quantitative Finance from Scratch, part 43: Black-Litterman. Fischer Black and Robert Litterman published it in 1992 as an improvement on the Markowitz optimizer. Markowitz needs each asset's expected return and volatility. Volatility is fairly easy to estimate, expected returns are very hard, and small errors in them push the weights to extremes. Black-Litterman starts from the market portfolio instead: all the money invested in a market, with each asset's weight equal to its share of the total. As in the CAPM part, this portfolio is optimal in equilibrium, so the model works backwards and asks which returns would make it optimal. The answer is π = δΣw: the market weights w, the covariance matrix Σ (how strongly the assets swing and move together) and the risk aversion δ (extra return demanded per unit of risk) give the implied returns π. Example with 60 % stocks and 40 % bonds, assuming 15 % volatility for stocks, 5 % for bonds, a correlation of 0.2 and δ = 2.5: stocks imply about 3.5 % above the risk free rate (3.525 %), bonds 0.475 %. Then you add your own view, for example stocks earn 6 %, and say how sure you are. The model mixes market and view like a weighted average. If you are as sure as the market (view uncertainty Ω = τσ² with τ = 0.05), stocks land at about 4.8 % (4.7625 %), exactly halfway. Without any view you get back the market portfolio. The code (bl_reel.py, 13 lines of plain Python without packages) is general on purpose: implied returns from risk aversion, covariance and weights, how much of your trust goes to your view, and the weighted average of market and view. For a single view on one asset this is exactly the full Black-Litterman formula. Source: Black, F. and Litterman, R. (1992), Global Portfolio Optimization, Financial Analysts Journal 48(5), 28-43. #quantfinance #finance #portfoliooptimization #markowitz #assetallocation Education only, not financial advice.

QuantFinanceToGo

20,000 просмотров • 7 дней назад

implied vol was 11.42% on Feb 19, 2020 realized vol over the next 30 days: 95.33% the market was pricing a normal week. what actually happened was one of the most violent moves in financial history that gap between implied and realized volatility is the single most important number quant desks watch implied vol is what options are pricing in for the future realized vol is what actually happened when implied is far below realized, options are cheap relative to what the market will actually do when implied is far above realized, options are expensive relative to what the market will actually do that spread has a name: the volatility risk premium Citadel, Susquehanna, Optiver built entire options desks around one question: what's the expected value of shorting overpriced vol vs buying underpriced vol? the scatter plot in the video shows every data point over years of history regression line: y = -0.73x + 18.5% translation: when implied vol is low, realized vol tends to explode. when implied vol is high, realized vol tends to collapse that's mean reversion in volatility itself. not price. vol retail buys calls hoping the stock goes up quant desks measure whether the option itself is mispriced relative to statistical expectation, and trade the premium one is a directional bet the other is arbitraging the gap between what people expect and what actually happens > volatility risk premium: documented in academic literature since the 1980s > average VRP on S&P 500: implied vol overprices realized vol by 3-5% historically > data: free from CBOE, Yahoo Finance, options chains > implementation: 20 lines of Python Feb 19, 2020 was a warning the math had been printing for weeks nobody in retail was reading it full breakdown in the video below
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implied vol was 11.42% on Feb 19, 2020 realized vol over the next 30 days: 95.33% the market was pricing a normal week. what actually happened was one of the most violent moves in financial history that gap between implied and realized volatility is the single most important number quant desks watch implied vol is what options are pricing in for the future realized vol is what actually happened when implied is far below realized, options are cheap relative to what the market will actually do when implied is far above realized, options are expensive relative to what the market will actually do that spread has a name: the volatility risk premium Citadel, Susquehanna, Optiver built entire options desks around one question: what's the expected value of shorting overpriced vol vs buying underpriced vol? the scatter plot in the video shows every data point over years of history regression line: y = -0.73x + 18.5% translation: when implied vol is low, realized vol tends to explode. when implied vol is high, realized vol tends to collapse that's mean reversion in volatility itself. not price. vol retail buys calls hoping the stock goes up quant desks measure whether the option itself is mispriced relative to statistical expectation, and trade the premium one is a directional bet the other is arbitraging the gap between what people expect and what actually happens > volatility risk premium: documented in academic literature since the 1980s > average VRP on S&P 500: implied vol overprices realized vol by 3-5% historically > data: free from CBOE, Yahoo Finance, options chains > implementation: 20 lines of Python Feb 19, 2020 was a warning the math had been printing for weeks nobody in retail was reading it full breakdown in the video below

delost

28,202 просмотров • 4 месяцев назад

➡️ Quant Finance from scratch Part 7: volatility Two simulated investments are both built to grow 8 % a year on average. One moves calmly, the other swings wildly. Step 1, what risk means. In quantitative finance, risk is how far the returns jump around their average, up as well as down. Step 2, measuring it. Take the daily returns and compute their standard deviation. For the calm one that is 0.25 % a day, for the wild one 1.99 %. Step 3, volatility. This number is usually quoted per year, and the square root rule from part 3 does the conversion: multiply by the square root of 252 trading days, which is about 15.87. The calm one has a volatility of 3.9 % a year, the wild one 31.6 %. Step 4, what the number means. The bell curve from part 4 turns it into a feeling. In about two years out of three, the calm one ends within 3.9 % of its 8 % average and the wild one within 31.6 %. In our run that held for 64.1 % and 65.8 % of 100,000 simulated years. Step 5, loss years. Over 100,000 simulated years each, the calm one loses money in 2.7 % of the years and the wild one in 46.8 %, with the same average return of about 8 % a year. Why quants care: volatility is everywhere in quantitative finance, from comparing investments to pricing options. This video is for education only, and nothing in it is financial advice. #quantfinance #volatility #risk #standarddeviation #python
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➡️ Quant Finance from scratch Part 7: volatility Two simulated investments are both built to grow 8 % a year on average. One moves calmly, the other swings wildly. Step 1, what risk means. In quantitative finance, risk is how far the returns jump around their average, up as well as down. Step 2, measuring it. Take the daily returns and compute their standard deviation. For the calm one that is 0.25 % a day, for the wild one 1.99 %. Step 3, volatility. This number is usually quoted per year, and the square root rule from part 3 does the conversion: multiply by the square root of 252 trading days, which is about 15.87. The calm one has a volatility of 3.9 % a year, the wild one 31.6 %. Step 4, what the number means. The bell curve from part 4 turns it into a feeling. In about two years out of three, the calm one ends within 3.9 % of its 8 % average and the wild one within 31.6 %. In our run that held for 64.1 % and 65.8 % of 100,000 simulated years. Step 5, loss years. Over 100,000 simulated years each, the calm one loses money in 2.7 % of the years and the wild one in 46.8 %, with the same average return of about 8 % a year. Why quants care: volatility is everywhere in quantitative finance, from comparing investments to pricing options. This video is for education only, and nothing in it is financial advice. #quantfinance #volatility #risk #standarddeviation #python

QuantFinanceToGo

21,400 просмотров • 1 месяц назад

➡️Quantitative Finance from Scratch, part 40: GJR GARCH. The goal is simple: forecast how big tomorrow's moves will be. Volatility comes in clusters, and plain GARCH uses that by building tomorrow's forecast from today's move squared and today's forecast. Squaring wipes out the sign, though, so a 4 % drop and a 4 % rise raise tomorrow's forecast by exactly the same amount. In real stock markets a drop raises volatility much more than a rise of the same size. One reason is leverage: when the price falls, the company's debt weighs more relative to its stock, so the stock itself becomes riskier. Glosten, Jagannathan and Runkle captured this in 1993 with one extra weight, gamma, that only switches on after a down day. The model is now known as GJR GARCH: tomorrow's variance = omega + (alpha + gamma x I) x today's move squared + beta x today's variance, where I is 1 after a down day and 0 otherwise. The code (gjr_reel.py, 16 lines of Python with numpy) uses typical values omega 0.02, alpha 0.02, gamma 0.12 and beta 0.90, in percent squared per day, so the normal level is a volatility of 1 % a day. After a 4 % rise: 0.02 + 0.02 x 16 + 0.90 x 1 = 1.24, a forecast of 1.11 %. After a 4 % drop: 0.02 + 0.14 x 16 + 0.90 x 1 = 3.16, a forecast of 1.78 %. The extra volatility is 0.11 against 0.78 percentage points, about seven times as much (6.8). Plain GARCH with the values from part 39 gives 1.58 % in both cases, so right after a sell off it underestimates the risk. Source: Glosten, L. R., Jagannathan, R. and Runkle, D. E. (1993), On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance 48(5), 1779 to 1801. Honest notes: the parameter values are typical textbook sizes, not estimates from real data. All market data in the video is simulated. #quantfinance #finance #volatility #riskmanagement #timeseries Education only, not financial advice.
1:36

➡️Quantitative Finance from Scratch, part 40: GJR GARCH. The goal is simple: forecast how big tomorrow's moves will be. Volatility comes in clusters, and plain GARCH uses that by building tomorrow's forecast from today's move squared and today's forecast. Squaring wipes out the sign, though, so a 4 % drop and a 4 % rise raise tomorrow's forecast by exactly the same amount. In real stock markets a drop raises volatility much more than a rise of the same size. One reason is leverage: when the price falls, the company's debt weighs more relative to its stock, so the stock itself becomes riskier. Glosten, Jagannathan and Runkle captured this in 1993 with one extra weight, gamma, that only switches on after a down day. The model is now known as GJR GARCH: tomorrow's variance = omega + (alpha + gamma x I) x today's move squared + beta x today's variance, where I is 1 after a down day and 0 otherwise. The code (gjr_reel.py, 16 lines of Python with numpy) uses typical values omega 0.02, alpha 0.02, gamma 0.12 and beta 0.90, in percent squared per day, so the normal level is a volatility of 1 % a day. After a 4 % rise: 0.02 + 0.02 x 16 + 0.90 x 1 = 1.24, a forecast of 1.11 %. After a 4 % drop: 0.02 + 0.14 x 16 + 0.90 x 1 = 3.16, a forecast of 1.78 %. The extra volatility is 0.11 against 0.78 percentage points, about seven times as much (6.8). Plain GARCH with the values from part 39 gives 1.58 % in both cases, so right after a sell off it underestimates the risk. Source: Glosten, L. R., Jagannathan, R. and Runkle, D. E. (1993), On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance 48(5), 1779 to 1801. Honest notes: the parameter values are typical textbook sizes, not estimates from real data. All market data in the video is simulated. #quantfinance #finance #volatility #riskmanagement #timeseries Education only, not financial advice.

QuantFinanceToGo

12,200 просмотров • 11 дней назад

If you've been trading for any amount of time, you're probably already aware of the concept of volatility and the impact it can have on the broader market. However, a concept that traders of all levels often miss is volatility supply. Volatility has a supply and demand curve, just like any other product, and it can be created or destroyed through a number of different means. Here's Cem Karsan 🥐 giving a great explanation of vol supply in response to a (very eloquent) YouTube comment asking about it! #StockMarket #Volatility #Investing #Finance #OptionsTrading
1:52

If you've been trading for any amount of time, you're probably already aware of the concept of volatility and the impact it can have on the broader market. However, a concept that traders of all levels often miss is volatility supply. Volatility has a supply and demand curve, just like any other product, and it can be created or destroyed through a number of different means. Here's Cem Karsan 🥐 giving a great explanation of vol supply in response to a (very eloquent) YouTube comment asking about it! #StockMarket #Volatility #Investing #Finance #OptionsTrading

tastylive

282,821 просмотров • 2 месяцев назад

➡️ Quantitative Finance from Scratch, part 39: GARCH. Markets show a clear pattern: calm weeks follow calm weeks, and high volatility days arrive in groups. This is called volatility clustering. Robert Engle introduced the idea in 1982 with the ARCH model (Econometrica), Tim Bollerslev extended it to GARCH in 1986 (Journal of Econometrics), and Engle received the 2003 Nobel Prize in economics for methods of analyzing time series with time-varying volatility. GARCH(1,1) builds tomorrow's variance, the square of volatility, from three parts: a small constant omega that pulls the forecast back toward a normal level, today's move squared times a weight alpha, so a big surprise raises tomorrow's forecast right away, and today's variance times a weight beta, the memory that keeps a high forecast high for a while. The code (garch_reel.py, 16 lines of Python with numpy) uses typical values omega 0.05, alpha 0.10 and beta 0.85, in percent squared per day. The normal level is a volatility of 1 % a day. After a drop of 4 % on a calm day, tomorrow's variance is 0.05 + 0.10 x 16 + 0.85 x 1 = 2.50, so the forecast volatility jumps to 1.58 %. The extra variance then halves every 13.5 trading days: the forecast for day 5 is 1.49 %, for day 10 1.39 % and for day 30 1.16 %. In 1,000,000 simulated days of the same model, a move above 2.5 % happens on 1.75 % of all days, but on 10.97 % of the days right after such a move, about 6.3 times as often. Risk managers use GARCH forecasts to update value at risk, and some funds scale their positions down when the forecast volatility rises. If you want the full picture, there is a longer GARCH video on the YouTube channel. Honest notes: all data in the video is simulated with the GARCH model itself, so the clustering is built in by design; in real markets volatility usually reacts more strongly to falls than to rises, which this simple symmetric model leaves out. The 3D landscape of columns (20 simulated stocks sharing one GARCH volatility) is an illustration with compressed heights, not to scale. The value at risk line uses 1.65 times the forecast volatility, a normal approximation for one day at 95 %. #quantfinance #garch #volatility #riskmanagement #finance Education only, not financial advice.
1:40

➡️ Quantitative Finance from Scratch, part 39: GARCH. Markets show a clear pattern: calm weeks follow calm weeks, and high volatility days arrive in groups. This is called volatility clustering. Robert Engle introduced the idea in 1982 with the ARCH model (Econometrica), Tim Bollerslev extended it to GARCH in 1986 (Journal of Econometrics), and Engle received the 2003 Nobel Prize in economics for methods of analyzing time series with time-varying volatility. GARCH(1,1) builds tomorrow's variance, the square of volatility, from three parts: a small constant omega that pulls the forecast back toward a normal level, today's move squared times a weight alpha, so a big surprise raises tomorrow's forecast right away, and today's variance times a weight beta, the memory that keeps a high forecast high for a while. The code (garch_reel.py, 16 lines of Python with numpy) uses typical values omega 0.05, alpha 0.10 and beta 0.85, in percent squared per day. The normal level is a volatility of 1 % a day. After a drop of 4 % on a calm day, tomorrow's variance is 0.05 + 0.10 x 16 + 0.85 x 1 = 2.50, so the forecast volatility jumps to 1.58 %. The extra variance then halves every 13.5 trading days: the forecast for day 5 is 1.49 %, for day 10 1.39 % and for day 30 1.16 %. In 1,000,000 simulated days of the same model, a move above 2.5 % happens on 1.75 % of all days, but on 10.97 % of the days right after such a move, about 6.3 times as often. Risk managers use GARCH forecasts to update value at risk, and some funds scale their positions down when the forecast volatility rises. If you want the full picture, there is a longer GARCH video on the YouTube channel. Honest notes: all data in the video is simulated with the GARCH model itself, so the clustering is built in by design; in real markets volatility usually reacts more strongly to falls than to rises, which this simple symmetric model leaves out. The 3D landscape of columns (20 simulated stocks sharing one GARCH volatility) is an illustration with compressed heights, not to scale. The value at risk line uses 1.65 times the forecast volatility, a normal approximation for one day at 95 %. #quantfinance #garch #volatility #riskmanagement #finance Education only, not financial advice.

QuantFinanceToGo

73,300 просмотров • 12 дней назад

🎥 Historical Volatility (HV) in cTrader - how it works and how to use it In this video, we explore Historical Volatility (HV) in cTrader - an indicator that measures past price fluctuations over a specific period, helping traders understand market variability and risk. You’ll learn where to find the Historical Volatility indicator in cTrader, how it is calculated using logarithmic price returns, standard deviation and annualisation, and how to customise settings such as standard deviation and bar history. We also look at how traders use HV to: • Identify rising volatility and expanding market swings • Recognise falling volatility and quieter market conditions • Confirm breakout conditions and trend continuation • Adjust protection and stop-loss placement based on market volatility • Combine HV with indicators such as ADX or moving averages • Use HV in cBots 📍 Timecodes 00:09 – Introduction: what is Historical Volatility (HV) 01:14 – Where to find Historical Volatility and how to customise its settings 01:34 – How Historical Volatility helps identify changing market conditions 02:29 – Using HV to confirm breakouts and trend continuation 03:39 – Using volatility to adjust protection and stop-loss placement 05:08 – Combining HV with other indicators and using it in cBots - Learn more about the Historical Volatility - - Join Discord - Don’t forget to like and share your thoughts in the comments! _____________________________________ 👉 Start Trading with cTrader - 👈
6:06

🎥 Historical Volatility (HV) in cTrader - how it works and how to use it In this video, we explore Historical Volatility (HV) in cTrader - an indicator that measures past price fluctuations over a specific period, helping traders understand market variability and risk. You’ll learn where to find the Historical Volatility indicator in cTrader, how it is calculated using logarithmic price returns, standard deviation and annualisation, and how to customise settings such as standard deviation and bar history. We also look at how traders use HV to: • Identify rising volatility and expanding market swings • Recognise falling volatility and quieter market conditions • Confirm breakout conditions and trend continuation • Adjust protection and stop-loss placement based on market volatility • Combine HV with indicators such as ADX or moving averages • Use HV in cBots 📍 Timecodes 00:09 – Introduction: what is Historical Volatility (HV) 01:14 – Where to find Historical Volatility and how to customise its settings 01:34 – How Historical Volatility helps identify changing market conditions 02:29 – Using HV to confirm breakouts and trend continuation 03:39 – Using volatility to adjust protection and stop-loss placement 05:08 – Combining HV with other indicators and using it in cBots - Learn more about the Historical Volatility - - Join Discord - Don’t forget to like and share your thoughts in the comments! _____________________________________ 👉 Start Trading with cTrader - 👈

cTrader

11,647 просмотров • 8 месяцев назад

When the market volatility is expressed in the form of dance.
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When the market volatility is expressed in the form of dance.

Vivek

15,210 просмотров • 5 месяцев назад

➡️ Part 28 of Quantitative Finance From Scratch: the low volatility anomaly. Here, risk means volatility, how much a stock's price swings. The CAPM (part 15) says expected return rises with beta, and wild stocks tend to have higher betas. Malcolm Baker, Brendan Bradley and Jeffrey Wurgler (Financial Analysts Journal, 2011) sorted all listed US stocks every month into five groups by the volatility of their monthly returns over the previous two to five years. From January 1968 to December 2008, $1 in the calmest fifth grew to $59.55, while $1 in the wildest fifth shrank to $0.58 (nominal, weighted by company size, rebalanced monthly, before trading costs; the authors note that trading costs were even higher for the wild stocks). The wildest fifth had the highest beta in the study, 1.71. Reason one is volatility drag (part 9): growth is roughly the average return minus half the variance. In our test run (assumed numbers: five groups with the same average return of 11 % a year and the volatilities of the study's groups, 13.1 % to 32 %, 41 years of monthly returns, 10,000 simulated histories each), a typical dollar ends at $63.29 in the calmest group and at $11.46 in the wildest. Luck still matters in a single history: with equal averages, the wildest group finished ahead of the calmest in about 22 % of the histories. In the study, the first four groups had almost the same average return above cash (about 4 to 5 % a year), so the drag explains most of their gap. The wildest group averaged 1.7 % a year less than cash, which the drag cannot explain. Reason two, as researchers suggest: many investors buy wild stocks like lottery tickets, hoping for a big win, so they pay too much and later earn less. The authors also point to fund managers who are judged against an index and rarely borrow. Low volatility funds use this idea, but the study covers one period of history, wild stocks soared in the technology bubble around 2000, and nobody knows whether the effect will hold in the future. Education only, not financial advice. #quantfinance #lowvolatility #factorinvesting #python #finance
1:46

➡️ Part 28 of Quantitative Finance From Scratch: the low volatility anomaly. Here, risk means volatility, how much a stock's price swings. The CAPM (part 15) says expected return rises with beta, and wild stocks tend to have higher betas. Malcolm Baker, Brendan Bradley and Jeffrey Wurgler (Financial Analysts Journal, 2011) sorted all listed US stocks every month into five groups by the volatility of their monthly returns over the previous two to five years. From January 1968 to December 2008, $1 in the calmest fifth grew to $59.55, while $1 in the wildest fifth shrank to $0.58 (nominal, weighted by company size, rebalanced monthly, before trading costs; the authors note that trading costs were even higher for the wild stocks). The wildest fifth had the highest beta in the study, 1.71. Reason one is volatility drag (part 9): growth is roughly the average return minus half the variance. In our test run (assumed numbers: five groups with the same average return of 11 % a year and the volatilities of the study's groups, 13.1 % to 32 %, 41 years of monthly returns, 10,000 simulated histories each), a typical dollar ends at $63.29 in the calmest group and at $11.46 in the wildest. Luck still matters in a single history: with equal averages, the wildest group finished ahead of the calmest in about 22 % of the histories. In the study, the first four groups had almost the same average return above cash (about 4 to 5 % a year), so the drag explains most of their gap. The wildest group averaged 1.7 % a year less than cash, which the drag cannot explain. Reason two, as researchers suggest: many investors buy wild stocks like lottery tickets, hoping for a big win, so they pay too much and later earn less. The authors also point to fund managers who are judged against an index and rarely borrow. Low volatility funds use this idea, but the study covers one period of history, wild stocks soared in the technology bubble around 2000, and nobody knows whether the effect will hold in the future. Education only, not financial advice. #quantfinance #lowvolatility #factorinvesting #python #finance

QuantFinanceToGo

11,000 просмотров • 26 дней назад

McCullough: Bitcoin Doesn’t Care About Your Cost Basis 🔊 Hedgeye CEO Keith McCullough made it clear this week: when downside accelerates, the market isn’t debating your cost basis or favorite “support level.” In fact, “the situation is accelerating at an accelerating rate,” explains McCullough. That’s why we focus on the rate of change, especially the volatility of volatility. “The volatility of volatility is going to get you to the right answer faster than the crowd.” Get Keith's quantitative Risk Range™ Signals and daily analysis on Bitcoin, Ethereum, Solana, and more, with our $BTC Trend Tracker: And for risk management insights you won’t get anywhere else, subscribe to The Macro Show:
3:39

McCullough: Bitcoin Doesn’t Care About Your Cost Basis 🔊 Hedgeye CEO Keith McCullough made it clear this week: when downside accelerates, the market isn’t debating your cost basis or favorite “support level.” In fact, “the situation is accelerating at an accelerating rate,” explains McCullough. That’s why we focus on the rate of change, especially the volatility of volatility. “The volatility of volatility is going to get you to the right answer faster than the crowd.” Get Keith's quantitative Risk Range™ Signals and daily analysis on Bitcoin, Ethereum, Solana, and more, with our $BTC Trend Tracker: And for risk management insights you won’t get anywhere else, subscribe to The Macro Show:

Hedgeye

13,872 просмотров • 9 месяцев назад