Accounting for Stochastic Interest Rates, Stochastic Volatility and a General Dependency Structure in the Valuation of Forward Starting Options

24 Pages Posted: 24 Mar 2010

See all articles by Alexander van Haastrecht

Alexander van Haastrecht

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

Antoon Pelsser

Maastricht University; Netspar

Multiple version iconThere are 2 versions of this paper

Date Written: August 1, 2009

Abstract

A quantitative analysis on the pricing of forward starting options under stochastic volatility and stochastic interest rates is performed. The main finding is that forward starting options not only depend on future smiles, but also directly on the evolution of the interest rates as well as the dependency structures between the underlying asset, the interest rates and the stochastic volatility: compared to vanilla options, dynamic structures such as forward starting options are much more sensitive to model specifications such as volatility, interest rate and correlation movements. We conclude that it is of crucial importance to take all these factors explicitly into account for a proper valuation and risk management of these securities. The performed analysis is facilitated by deriving closed-form formulas for the valuation of a forward starting options, hereby taking the stochastic volatility, stochastic interest rates as well the dependency structure between all these processes explicitly into account. The valuation framework is derived using a probabilistic approach, enabling a fast and efficient evaluation of the option price by Fourier inverting the forward starting characteristic functions.

Keywords: Forward-Starting Options, Stochastic Interest Rates, Stochastic Volatility, Correlation Risk, Fourier Inversion

Suggested Citation

van Haastrecht, Alexander and van Haastrecht, Alexander and Pelsser, Antoon A. J., Accounting for Stochastic Interest Rates, Stochastic Volatility and a General Dependency Structure in the Valuation of Forward Starting Options (August 1, 2009). Netspar Discussion Paper No. 08/2009-047, Available at SSRN: https://ssrn.com/abstract=1576617 or http://dx.doi.org/10.2139/ssrn.1576617

Alexander Van Haastrecht

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

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Delta Lloyd ( email )

Spaklerweg 4
Amsterdam, Noord-Holland 1096BA
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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