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➡️ 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. The
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➡️ Quantitative Finance from Scratch, part 38: the volatility smile Read the implied volatility out of the option price at every strike and every expiry, and the Black-Scholes model says you should get one flat surface. Real option markets do not give a flat surface. Implied volatility often rises at both ends, so the curve across strikes looks like a smile, hence the name. For options on a stock index the left end, at the low strikes, is much higher, which is called the skew. Low strikes belong
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