Integrating Various Stochastic Factors

In this chapter we summarize the different option pricing models discussed previously, and build up an unified comprehensive option pricing framework. We have generally two approaches to integrating various stochastic factors: the modular approach and the time-change approach. While the modular approach has a simple, clear and transparent structure, and is also designed for practical implementations, the approach based on time-change is more technical and may embrace some nested factors. To show the large accommodation of the new pricing framework with CFs, we use four volatility specifications, four interest rate specifications, four Poisson jump specifications and four Lévy jump specifications to develop 4×4×4×4=256 different option pricing models. In fact, the number of possible pricing models by assembling different stochastic factors via CFs is much larger. Additionally, it can be shown that the pricing kernels for option pricing and bond pricing are identical if volatility and interest rate are specified to follow a same stochastic process. Finally, from the various points of view of practical applications, I give some criterions for choosing “ideal” models.