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

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2018

Author

Yilmaz, Bilgi

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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.

Subject Keywords

Malliavin calculus, Bismut-Elworthy-Li formula, Computation of greeks;, Hybrid stochastic volatility models

URI

https://hdl.handle.net/11511/51649

Journal

Modern Stochastics: Theory and Applications

DOI

https://doi.org/10.15559/18-vmsta100

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. Yilmaz, “Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus,” Modern Stochastics: Theory and Applications, pp. 145–165, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51649.