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

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YILMAZ B.

MODERN STOCHASTICS-THEORY AND APPLICATIONS, vol.5, no.2, pp.145-165, 2018 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.15559/18-vmsta100
  • Journal Name: MODERN STOCHASTICS-THEORY AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.145-165
  • Keywords: Malliavin calculus, Bismut-Elworthy-Li formula, computation of greeks, hybrid stochastic volatility models
  • Middle East Technical University Affiliated: Yes

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.