Introduction to Lévy processes
The classical Black-Scholes model employs the Brownian motion as the driving stochastic process of asset prices. Empirical evidence has pointed out that such an assumption does not provide an accurate description of financial data and has promoted the development of more flexible models. This chapter presents the fundamentals of Lévy processes and option pricing under such stochastic processes. Since this chapter is intended as an informal introduction to Lévy processes, many of the proofs are omitted: for a complete treatment of the theory we refer to the classical monographs by Bertoin , Sato , Jacod and Shiryaev .
KeywordsOption Price Implied Volatility Characteristic Exponent Stochastic Volatility Model Compound Poisson Process
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