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➡️ 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....

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➡️ 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 次观看 • 12 天前

➡️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 次观看 • 11 天前

➡️ 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 their own views, buy and sell options, and supply and demand set the price. Put that market price into the formula and solve it backwards for the volatility, and you get the implied volatility. Our test run (impliedvol.py, 16 lines of plain Python): stock 100, strike 100, rate 5 %, 1 year, and a call that costs 12 dollars on the market. The volatility sits in several places of the formula, so there is no way to solve for it by hand, but the price always rises with the volatility. A bisection search tries the middle of the range (50 %, 25 %, 12.5 % and so on) and halves the range each time. After 10 steps the price fits to half a cent, and the implied volatility is 24.1 %. Every strike and every expiry date has its own implied volatility. Together all these values form the implied volatility surface. Historical volatility, measured from past returns, serves as a comparison, and as the estimate when no options trade. Honest notes: the smile, the expiry curve and the 3D surface in the video are an illustration in the typical shape for index options, anchored at our test run, and contain no market data. The price paths and the past returns are simulated. Implied volatility shows how the market prices the expected swing, and the real swing can turn out larger or smaller. #quantfinance #impliedvolatility #options #blackscholes #finance

QuantFinanceToGo

51,900 次观看 • 21 天前

➡️ 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 次观看 • 15 天前

➡️ 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 次观看 • 7 天前

➡️ 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 次观看 • 2 天前

I think May and June could be brutal for crypto, and in this video I walk through exactly why I still believe BTC could push all the way down to $38,555 before this bear market leg is done. The core of the argument comes from the crypto calendar and how the last real bottom years behaved, especially when you compare monthly closes with the full wick-to-wick volatility inside those candles. I break down what those historical averages imply for BTC first, then apply the same lens to ETH and the broader market. The important point is not just that monthly closes could be red. It is that the intramonth volatility can get much uglier than the close alone suggests, which is why a move that looks manageable on paper can still feel like a bloodbath in real time. I also zoom out to TOTALES and the smaller-cap market to show how deep the damage could go if the same kind of bear-market behavior repeats. That is where the opportunity comes in too. If this forecast is even directionally right, the next two months could create some of the best accumulation windows of the cycle, but only for people who stay patient, think probabilistically, and avoid pretending projections are guarantees. The biggest takeaway is that this is a forecast, not a certainty. July has historically looked stronger, but I do not treat that as proof the full bottom is in. Right now I am using the best historical data we have to map the downside, prepare for volatility, and think ahead instead of reacting after the damage is already done. Crypto Calendar: Chapters: 00:00 Bitcoin to $38,555 by June? 01:48 BTC May and June historical forecast 03:19 Bitcoin volatility and lower wick projections 06:40 June could be even worse for BTC 10:47 Why this data comes from The Better Traders Club 12:34 Ethereum May and June forecast 15:30 ETH volatility and the $1,000 target 20:02 What TOTALES shows about the whole crypto market 23:29 TOTALES May and June downside projections 27:04 TOTALES vs TOTALLY50 vs TOTALLY100 explained 31:39 TOTALLY50 forecast and mid-cap risk 34:51 TOTALLY100 forecast and smaller-cap risk 36:21 Why July could bring a bounce 37:40 These are projections, not guarantees 40:02 How traders should prepare 41:48 Trading volatility and final thoughts 🎲 Play Moonin Papa BINGO with today's video: 💹 Take Your Trading to the Next Level! 💰 Sign up & Trade on Kraken 👉 🥇 Toobit: $15k Bonus 👉 🥈 TBO indicator: identify trends early, confirm breakouts, and maximize profits by staying in the trend 👉 📚 Learn Proven Crypto Strategies: Master bot trading, scalping, day trading, and swing trading with our courses: 🌐 Stay Connected: Follow me for market updates and insights across platforms:

Aaron Dishner

17,844 次观看 • 6 个月前

➡️ Quantitative Finance from scratch part 12 closes season 1. Every part was one step in a single story about a bet with an edge, and every number below comes from that part's own run. Part 1, expected value: a $1 bet on red wins 18 times out of 37, so it loses 2.7 cents on average, and over a million bets the casino made $27,288. Part 2, the random walk: coin flips add up to something that looks like a stock chart, and the same edge becomes a drift of 2.7 cents per step. Part 3, the square root rule: after 100 random steps the typical distance is about 10, because randomness grows with the square root of time. Part 4, the bell curve: many small random steps build it, with 68 % of results within one standard deviation. Part 5, returns: percent moves multiply, so after -50 % you need +100 % to get back. Part 6, present value: at 5 % interest, $100 paid in ten years is worth $61.39 today. Part 7, volatility: two investments with the same average swing about 4 % and 32 % a year. Part 8, the Sharpe ratio (William F. Sharpe, 1966): extra return per unit of risk, 0.36 for the wild investment and 0.99 for the calm one. Part 9, volatility drag: +50 % and then -50 % leaves you 25 % down. Part 10, correlation: the less two assets move together, the less a 50/50 mix swings, from 19 % down to 10 %. Part 11, diversification: ten assets cut the risk from 20 % to 12.2 %, above a floor of 11 % that the shared market sets (Markowitz, "Portfolio Selection", Journal of Finance, 1952). The big picture: how big the edge is, how much it swings, and how much of that swing you can spread away. Season 2 brings portfolios, bets and evidence. This video is for education only, and nothing in it is financial advice. #quantfinance #finance #riskmanagement #portfolio #probability

QuantFinanceToGo

112,700 次观看 • 1 个月前

➡️ Quantitative Finance From Scratch, Part 21: Linear Regression in finance Linear regression finds the straight line that best describes how one quantity moves with another. In finance, that is often a stock's daily return against the market's daily return. Least squares: for every day, you measure how far the real return lies from the line, square that distance and add everything up. The best line makes this sum as small as possible. The line has two numbers. The slope is the beta from Part 14: how strongly the stock follows the market. The intercept is alpha: what the stock earns on average on a day when the market does not move. What the line cannot explain is the residual, and R² tells you which share of the swings (the variance) the line explains, from 0 for nothing to 1 for everything. In this video we simulate two years (504 trading days) of a market and a stock with a built-in beta of 1.2, a second factor with a beta of 0.6 and no alpha. The line finds a beta of 1.26 (the 1.2 lies within the range of chance for two years of data), an alpha of +0.05% a day and an R² of 52%. With two inputs, the line becomes a plane: betas 1.27 and 0.60, R² 63%. Quants use regression to estimate betas, to size hedges, to test whether a strategy earns more than its risk, and to check whether two assets really move together. The limits: a regression only finds a relationship in the data you give it. It does not prove that one thing causes the other, a few extreme days can pull the line (three invented extreme days move our slope from 1.26 to 1.10), and a relationship from the past can change. Education only, not financial advice. #quantitativefinance #quant #finance #regression #beta

QuantFinanceToGo

59,100 次观看 • 1 个月前

➡️ Quantitative Finance from Scratch, part 47: What does a market maker actually do? A market maker is a trading firm that always provides two prices for a stock: the ask (higher, what you pay when you buy) and the bid (lower, what you get when you sell). When you trade as a retail investor, the other side is usually a market maker. It stands in the middle, so someone is always there to trade with you. This is called providing liquidity. In return, it earns the spread (spread = ask − bid). Buy at 99.98 dollars, sell at 100.02 dollars, and it earns four cents per share. That sounds tiny, but it repeats all day across many stocks. The job comes with two big risks. Inventory: when many people sell at once, the market maker ends up holding a lot of stock, and if the price then falls, it loses money (P&L = cash + inventory × fair price). Informed traders: someone who hears news first sells to the market maker right before the price drops. A good market maker adjusts its two prices all day, moving them with its inventory and widening the gap when the risk grows. On many exchanges, official market makers promise to quote within a maximum spread and pay lower fees in return. The code (mm_reel.py, 16 lines of plain Python without packages) is general on purpose: two quotes around a mid price, what happens when a customer buys or sells, the profit and loss, and a quote shifted with the inventory. If you want to go deeper, check out the full course I built: quantfinancetogo.com #quantfinance #marketmaking #marketmaker #finance #python Education only, not financial advice.

QuantFinanceToGo

30,200 次观看 • 2 天前