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

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YILMAZ B.

MODERN STOCHASTICS-THEORY AND APPLICATIONS, cilt.5, sa.2, ss.145-165, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.15559/18-vmsta100
  • Dergi Adı: MODERN STOCHASTICS-THEORY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.145-165
  • Anahtar Kelimeler: Malliavin calculus, Bismut-Elworthy-Li formula, computation of greeks, hybrid stochastic volatility models
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.