Titlebook: Derivative Security Pricing; Techniques, Methods Carl Chiarella,Xue-Zhong He,Christina Sklibosios N Book 2015 Springer-Verlag Berlin Heide

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Option Pricing Under Jump-Diffusion Processespricing model, we provide an option pricing integro-partial differential equations and a general solution. We also examine alternative ways to construct the hedging portfolio and to price option when the jump sizes are fixed.

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Volatility Smiless which may underestimate the size of the smile. We then develop an approach to calibrate the smile by choosing the volatility function as a deterministic function of the underlying asset price and time so as to fit the model option price to the observed volatility smile.

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Partial Differential Equation Approach Under Geometric Jump-Diffusion Processng asset follows a diffusion process. The second is the direct approach using the expectation operator expression that follows from the martingale representation. We also show how these two approaches are connected.

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An Initial Attempt at Pricing an Optionat investors are risk neutral and using the Kolmogorov equation for the conditional probability, we demonstrate how the Black–Scholes option formula can be arrived. We also illustrate how the option price can be viewed in a quite natural way as a martingale and the Feynman–Kac formula, two very impo