Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus
Volume 5, Issue 2 (2018), pp. 145–165
Pub. online: 24 April 2018
Type: Research Article
Open Access
Open Access
Received
2 May 2017
2 May 2017
Revised
26 February 2018
26 February 2018
Accepted
30 March 2018
30 March 2018
Published
24 April 2018
24 April 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.
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