Monte Carlo Pricing in the Schöbel-Zhu Model and its Extensions

23 Pages Posted: 23 Mar 2010  

Alexander van Haastrecht

Delta Lloyd; VU University Amsterdam - Faculty of Economics and Business Administration

Roger Lord

Cardano Risk Management

Antoon Pelsser

Maastricht University; Netspar

Multiple version iconThere are 2 versions of this paper

Date Written: August 1, 2009

Abstract

In this paper we propose a simulation algorithm for the Schöbel-Zhu (1999) model and its extension to include stochastic interest rates, the Schöbel-Zhu-Hull-White model as considered in Van Haastrecht et al. (2009). Both schemes are derived by analyzing the lessons learned from the Andersen scheme on how to avoid the so-called leaking correlation phenomenon in the simulation of the Heston (1993) model. All introduced schemes are Exponentially Affine in Expectation (EAE), which greatly facilitates the derivation of a martingale correction. In addition we study the regularity of each scheme. The numerical results indicate that our scheme consistently outperforms the Euler scheme. For a special case of the Schöbel-Zhu model which coincides with the Heston model, our scheme performs similarly to the QE-M scheme of Andersen (2008). The results reaffirm that when simulating stochastic volatility models it is of the utmost importance to match the correlation between the asset price and the stochastic volatility process.

Keywords: Stochastic Volatility, Stochastic Interest Rates, Schöbel-Zhu, Heston, Hull-White, Discretisation

Suggested Citation

van Haastrecht, Alexander and Lord, Roger and Pelsser, Antoon, Monte Carlo Pricing in the Schöbel-Zhu Model and its Extensions (August 1, 2009). Netspar Discussion Paper No. 08/2009-046. Available at SSRN: https://ssrn.com/abstract=1576581 or http://dx.doi.org/10.2139/ssrn.1576581

Alexander Van Haastrecht

Delta Lloyd ( email )

Spaklerweg 4
Amsterdam, Noord-Holland 1096BA
Netherlands

VU University Amsterdam - Faculty of Economics and Business Administration ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Roger Lord

Cardano Risk Management ( email )

Rotterdam 3011 AA
Netherlands

Antoon A. J. Pelsser (Contact Author)

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Paper statistics

Downloads
89
Rank
53,293
Abstract Views
589