10. Option Pricing
This chapter is devoted to the pricing of options. An option derives its value from an underlying asset, but its payoff is a nonlinear function of the underlying asset price, and so the option price is also a nonlinear function of the underlying asset price. This nonlinearity adds complications to pricing and risk management. In this chapter we will first introduce the binomial tree approach and the Black-Scholes-Merton (BSM) approach to option pricing. We then extend the BSM model by allowing for skewness and kurtosis in returns as well as for time-varying volatility. We will also introduce the ad hoc implied volatility function (IVF) approach to option pricing. The IVF method is not derived from any coherent theory but it ...
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