Edited by Adrian R. Bell, Chris Brooks and Marcel Prokopczuk
Chapter 6: Derivatives pricing with affine models and numerical implementation
Affine models are popular in finance, especially since the publication of Duffie et al. (2000). They represent a compromise between tractibility and empirical complexity. The characteristic function of the underlying dynamics in affine models is an exponential affine function of the state variables. As a result, the price and characteristic function of a contingent claim can be expressed as an integral and evaluated numerically. In this chapter we present the most popular theory of derivatives pricing with affine models and explain their numerical implementation. The remainder of this chapter is outlined as follows. In section 6.2, we present some stochastic differential equations (SDE) that underly well-known affine models in finance. Section 6.3 links the SDE of the underlying dynamics to the partial differential equation (PDE) of the characteristic function. Some pricing examples are presented in section 6.4. Section 6.5 summarizes the reasons why affine models are so attractive in option pricing, and finally, section 6.6 introduces two different ways for calculating the option price numerically.
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