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A Course in Financial Calculus by Alison Etheridge

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7 Bigger models

Summary

Having applied our basic Black–Scholes model to the pricing of some exotic options, we now turn to more general market models.

In §7.1 we replace the (constant) parameters that characterised our basic Black–Scholes model by previsible processes. Under appropriate boundedness assumptions, we then repeat our analysis of Chapter 5 to obtain the fair price of an option as the discounted expected value of the claim under a martingale measure. In general this expectation must be evaluated numerically. We also make the connection with a generalised Black–Scholes equation via the Feynman–Kac Stochastic Representation Theorem.

Our models so far have assumed that the market consists of a single stock and a riskless cash bond. More ...

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