Computation of Malliavin Greeks in Hybrid StochasticVolatility Models

2015-05-16
Yılmaz, Bilgi
Yolcu Okur, Yeliz
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 not exist. However, an approximated value can be computed by using Malliavin calculus tools and Monte Carlo simulations. In this study we compute the Malliavin Greeks in the setting of hybrid stochastic volatility models and analyze the effect of the correlation, among the Brownian motions, on these Greeks.

Suggestions

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 ...
Modelling and implementation of local volatility surfaces
Animoku, Abdulwahab; Yolcu Okur, Yeliz; Uğur, Ömür; Department of Financial Mathematics (2014)
In this thesis, Dupire local volatility model is studied in details as a means of modeling the volatility structure of a financial asset. In this respect, several forms of local volatility equations have been derived: Dupire's local volatility, local volatility as conditional expectation, and local volatility as a function of implied volatility. We have proven the main results of local volatility model discussed in the literature in details. In addition, we have also proven the local volatility model under ...
Stochastic volatility and stochastic interest rate model with jump and its application on General Electric data
Celep, Betül; Hayfavi, Azize; Department of Financial Mathematics (2011)
In this thesis, we present two different approaches for the stochastic volatility and stochastic interest rate model with jump and analyze the performance of four alternative models. In the first approach, suggested by Scott, the closed form solution for prices on European call stock options are developed by deriving characteristic functions with the help of martingale methods. Here, we study the asset price process and give in detail the derivation of the European call option price process. The second appr...
Computation of option greeks under hybrid stochastic volatility models via Malliavin calculus
Yilmaz, Bilgi (VTeX, 2018)
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...
Analysis of stochastic and non-stochastic volatility models.
Özkan, Pelin; Ayhan, Hüseyin Öztaş; Department of Statistics (2004)
Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order...
Citation Formats
B. Yılmaz and Y. Yolcu Okur, “Computation of Malliavin Greeks in Hybrid StochasticVolatility Models,” presented at the 55th Meeting of the EWGCFM (2015), Ankara, Türkiye, 2015, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/71189.