Computation of Option Greeks Under Hybrid Stochastic Volatility Models Via Malliavin Calculus

Modern Stochastics: Theory and Applications 5 (2), 145–165, 2018

21 Pages Posted: 3 Apr 2020

See all articles by Bilgi Yilmaz

Bilgi Yilmaz

Middle Eastern Technical University Ankara

Date Written: April 24, 2018

Abstract

This study introduces computation of option sensitivities (Greeks) using the Malliavin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic volatility model and a stochastic interest rate model, respectively. Therefore, it integrates the recent developments in the Malliavin calculus for the computation of Greeks: Delta, Vega, and Rho and it extends the method slightly. The main results show that Malliavin calculus allows a running Monte Carlo (MC) algorithm to present numerical implementations and to illustrate its effectiveness. The main advantage of this method is that once the algorithms are constructed, they can be used for numerous types of option, even if their payoff functions are not differentiable.

Keywords: Malliavin Calculus, Bismut–Elworthy–Li Formula, Computation of Greeks, Hybrid Stochastic Volatility Models

JEL Classification: G32, D53, B16

Suggested Citation

Yilmaz, Bilgi, Computation of Option Greeks Under Hybrid Stochastic Volatility Models Via Malliavin Calculus (April 24, 2018). Modern Stochastics: Theory and Applications 5 (2), 145–165, 2018, Available at SSRN: https://ssrn.com/abstract=3551853

Bilgi Yilmaz (Contact Author)

Middle Eastern Technical University Ankara ( email )

Ankara
Turkey

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