#hedging
➡️ 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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