Pricing Long-Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility

28 Pages Posted: 29 Apr 2008 Last revised: 9 May 2011

See all articles by Alexander van Haastrecht

Alexander van Haastrecht

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

Roger Lord

Cardano Risk Management

Antoon Pelsser

Maastricht University; Netspar

David Schrager

Longitude Solutions

Date Written: January 10, 2005

Abstract

In this paper we extend the stochastic volatility model of Schöbel and Zhu (1999) by including stochastic interest rates. Furthermore we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a correlation between the instantaneous interest rates, the volatilities and the underlying stock returns. By deriving the characteristic function of the log-asset price distribution, we are able to price European stock options in closed-form by Fourier inversion. Furthermore we present a Foreign Exchange generalization and show how the pricing of Forward-starting options like cliquets can be performed. Additionally we discuss the practical implementation of these new models.

Keywords: Stochastic volatility, Stochastic interest rates, Schöbel-Zhu, Hull-White, Foreign Exchange, Forward starting options

JEL Classification: C10

Suggested Citation

van Haastrecht, Alexander and Lord, Roger and Pelsser, Antoon A. J. and Schrager, David, Pricing Long-Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility (January 10, 2005). Insurance: Mathematics and Economics, Vol. 45, No. 3, 2009, Available at SSRN: https://ssrn.com/abstract=1125590

Alexander Van Haastrecht (Contact Author)

Delta Lloyd ( email )

Spaklerweg 4
Amsterdam, Noord-Holland 1096BA
Netherlands

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Roger Lord

Cardano Risk Management ( email )

Rotterdam 3011 AA
Netherlands

Antoon A. J. Pelsser

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

David Schrager

Longitude Solutions ( email )

Herengracht 116c
Amsterdam, 1015 BT
Netherlands
+31624521678 (Phone)

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