Statistical Methods in Finance 2017

Abstract

Saddlepoint approximation methods for pricing financial options on discrete realized variance

by Yue Kuen Kwok

The saddlepoint approximation is an effective analytic approximation approach for approximating a density in the tails of the distribution from its associated moment generating function or cumulant generating function. Pricing of a financial option requires valuation of the discounted expectation under a pricing measure of the tail distribution of the terminal price of a risky asset. We consider the saddlepoint approximation methods for pricing financial options whose payoffs depend on the discrete realized variance of the underlying asset price process. Under the Levy models and stochastic volatility models with jumps, we manage to obtain the saddlepoint approximation formulas for pricing variance products and volatility derivatives using the small time asymptotic approximation of the Laplace transform of the discrete realized variance. We examine numerical accuracy and reliability of various types of the saddlepoint approximation techniques when applied to pricing derivatives on discrete realized variance under different types of asset price processes. The limitations of the saddlepoint approximation methods in pricing variance products and volatility derivatives are also discussed.

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