Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus

• Main Author: Bilgi Yilmaz
• Format: Article
• Language: English
• Published: VTeX 2018-04-01
• Series: Modern Stochastics: Theory and Applications
• Subjects: Malliavin calculus; Bismut–Elworthy–Li formula; computation of greeks; hybrid stochastic volatility models
• Online Access: https://vmsta.vtex.vmt/doi/10.15559/18-VMSTA100

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.