November 2012
Beginner
733 pages
27h 41m
English
Content preview from Encyclopedia of Financial Models III
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Conditional Expectation and Change of Measure
Abstract: The current price of an option is obtained by the conditional expectation of the payoff function under the risk-neutral measure. The risk-neutral measure is the measure equivalent to the real market measure under which the discounted price process of the underlying stock becomes a martingale. In the Black-Scholes model, the risk-neutral measure can be obtained by the Girsanov theorem. The Esscher transform has been used to find the risk-neutral measure for the continuous Lévy process models. The general theory of the Esscher transform is applied to find the risk-neutral measure under tempered stable Lévy process models.
In this entry, we present some issues in stochastic processes. We begin by defining events of a probability space mathematically, and then discuss the concept of conditional expectation. We then explain two important notions for stochastic processes: martingale properties and Markov properties. The ...