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Stochastic Volatility Meets Mean-Variance Analysis

Wilmott does not like the market price of risk. He says so right at the start of Chapter 54, and his reasoning is solid. The market price of volatility risk is not directly observable. You can only back it out from option prices, and that only works if the people setting those prices are using the same model you are. If you refit the model a few days later and get a different answer, was the market wrong before? Or is it wrong now? You end up chasing your own tail.

Empirical Volatility: What the Data Actually Shows

Most people who model stochastic volatility start by writing down a nice-looking equation and then try to fit it to data. Wilmott thinks this is backwards. In Chapter 53, he starts with the data and builds the model from the ground up. It is a refreshingly practical approach. Instead of picking a model because it is mathematically convenient, he asks: what does volatility actually do?

Uncertain Parameters: What if You Don't Know the Volatility?

Let us start with an uncomfortable truth. The Black-Scholes equation has three main parameters: volatility, interest rate, and dividend yield. Of these three, not a single one is known with certainty. Sure, you know today’s stock price. You know the expiry date. But the stuff that actually matters for pricing? You are guessing. Chapter 52 of Wilmott’s book takes this discomfort and turns it into a pricing framework.

Stochastic Volatility: When Volatility Itself Is Random

Volatility is not constant. We knew that already. The deterministic volatility surface tries to fix this by making volatility a function of stock price and time. But the surface changes every time you recalibrate. The model is fundamentally incomplete.

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