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


Alexander Van Haastrecht


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

Roger Lord


Cardano Risk Management

Antoon Pelsser


Maastricht University; Netspar

August 1, 2009

Netspar Discussion Paper No. 08/2009-046

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.

Number of Pages in PDF File: 23

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

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Date posted: March 23, 2010  

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: http://ssrn.com/abstract=1576581 or http://dx.doi.org/10.2139/ssrn.1576581

Contact Information

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
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