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Friday 23 October 2026 15:32:24 GMT
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In this video, we derive the Black-Scholes formula from first principles using the concept of replicating portfolios, showing why option pricing does not depend on expected stock returns. We build the intuition from a one-step tree up to continuous time, explain how dynamic hedging balances gamma risk against time decay, and examine both the Merton default model and where the formula breaks down in the post-1987 volatility smile. #BlackScholes #OptionPricing #QuantitativeFinance #AppliedMathematics
In this video, we derive the Black-Scholes formula from first principles using the concept of replicating portfolios, showing why option pricing does not depend on expected stock returns. We build the intuition from a one-step tree up to continuous time, explain how dynamic hedging balances gamma risk against time decay, and examine both the Merton default model and where the formula breaks down in the post-1987 volatility smile. #BlackScholes #OptionPricing #QuantitativeFinance #AppliedMathematics
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