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

25 Pages Posted: 11 Oct 2009 Last revised: 4 Oct 2011

See all articles by Alexander van Haastrecht

Alexander van Haastrecht

Vrije Universiteit Amsterdam, School of Business and Economics; Delta Lloyd

Roger Lord

Cardano Risk Management

Antoon Pelsser

Maastricht University; Netspar

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Date Written: October 8, 2009


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

JEL Classification: C1

Suggested Citation

van Haastrecht, Alexander and van Haastrecht, Alexander and Lord, Roger and Pelsser, Antoon A. J., Monte Carlo Pricing in the Schöbel-Zhu Model and its Extensions (October 8, 2009). Available at SSRN: or

Alexander Van Haastrecht (Contact Author)

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Roger Lord

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Antoon A. J. Pelsser

Maastricht University ( email )

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