Computation of the Delta of European options under stochastic volatility models

Date

2018-06-01

Author

Yolcu Okur, Yeliz
Sayer, Tilman
Yılmaz, Bilgi
Inkaya, B. Alper

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

218
views

0
downloads

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.

Subject Keywords

Greeks, Malliavin calculus, Stochastic volatility

URI

https://hdl.handle.net/11511/57677

Journal

COMPUTATIONAL MANAGEMENT SCIENCE

DOI

https://doi.org/10.1007/s10287-018-0316-y

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

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...
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 ...
A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance Savku, Emel; Weber, Gerhard Wilhelm (2018-11-01) We study a stochastic optimal control problem for a delayed Markov regime-switching jump-diffusion model. We establish necessary and sufficient maximum principles under full and partial information for such a system. We prove the existence-uniqueness theorem for the adjoint equations, which are represented by an anticipated backward stochastic differential equation with jumps and regimes. We illustrate our results by a problem of optimal consumption problem from a cash flow with delay and regimes.
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...
Advances and applications of stochastic Ito-Taylor approximation and change of time method in the financial sector Öz, Hacer; Weber, Gerhard Wilhelm; Department of Financial Mathematics (2013) In this thesis, we discuss two different approaches for the solution of stochastic differential equations (SDEs): Ito-Taylor method (IT-M) and change of time method (CT-M). First approach is an approximation in space-domain and the second one is a probabilistic transformation in time-domain. Both approaches may be considered to substitute SDEs for more “practical” representations and solutions. IT-M was most studied for one-dimensional SDEs. The main aim of this work is to extend the theory of one-dimension...

Citation Formats

Y. Yolcu Okur, T. Sayer, B. Yılmaz, and B. A. Inkaya, “Computation of the Delta of European options under stochastic volatility models,” COMPUTATIONAL MANAGEMENT SCIENCE, pp. 213–237, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57677.