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

2018
Yilmaz, Bilgi
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.
Modern Stochastics: Theory and Applications

Suggestions

 Computation of the Delta of European options under stochastic volatility models Yolcu Okur, Yeliz; Sayer, Tilman; Yılmaz, Bilgi; Inkaya, B. Alper (2018-06-01) We employ Malliavin calculus techniques to compute the Delta of European type options in the presence of stochastic volatility. We obtain a general formula for the Malliavin weight and apply the derived formula to the well known models of Stein-Stein and Heston in order to show the numerical accuracy and efficiency of our approach.
 Computation of Hedging Coefficients for Mortgage Default and Prepayment Options: Malliavin Calculus Approach YILMAZ, BİLGİ; Kestel, Sevtap Ayşe (2019-11-01) This study explores the hedging coefficients of the financial options to default and to prepay embedded into mortgage contracts based on the change in spot rate, underlying house price and its volatility. In the computations, the finite-dimensional Malliavin calculus is applied since the distribution of both options is unknown and their payoffs are non-differentiable. Naturally, the hedging coefficients are obtained as a product of option's payoff and an independent weight, which permits the user to derive ...
 Computation of the greeks in black-scholes-merton and stochastic volatility models using malliavin calculus Yılmaz, Bilgi; Yolcu Okur, Yeliz; Department of Financial Mathematics (2014) The computation of the Greeks of options is an essential aspect of financial mathematics. The investors use the information gained from this aspect for hedging purposes or to decide whether to invest in an option or not. However, computation of the Greeks is not straightforward in some cases due to technical difficulties. For instance, the value function of some options are complicated or moreover in some cases they might not have a closed form solution which makes the computation of their Greeks cumbersome...
 Application of stochastic volatility models with jumps to BIST options Rahiminejat, Monireh; Sezer, Ali Devin; Department of Financial Mathematics (2017) This thesis gives a derivation of call and put option pricing formulas under stochastic volatility models with jumps; the precise model is a combination of Merton and Heston models. The derivation is based on the computation of the characteristic function of the underlying process. We use the derived formulas to fit the model to options written on two stocks in the BIST30 index covering the first two months of 2017. The fit is done by minimizing a weighted \$L_2\$ distance between the observed prices and the ...
 Computation of Malliavin Greeks in Hybrid StochasticVolatility Models Yılmaz, Bilgi; Yolcu Okur, Yeliz (2015-05-16) Contrary to Black-Scholes model in stochastic volatility models, the stock price’s volatility assumed to be a stochastic process and the Brownian motions of volatility and stock price process are correlated with each other. Moreover, in some models, called hybrid stochastic volatility models, the interest rate also assumed to be a stochastic process. Because of the stochastic volatility, stochastic interest rate and correlated Brownian motions, a closed form solution for the Greeks of the options usually do...
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.