Accounting for stochastic interest rates, stochastic volatility and general correlation structure in the valuation of forward starting options

A. van Haastrecht, A. Pelsser

Research output: Contribution to JournalArticleAcademicpeer-review

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 among 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 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. © 2010 Wiley Periodicals, Inc.
Original languageEnglish
Pages (from-to)103-125
JournalThe Journal of Futures Markets
Volume31
Issue number2
DOIs
Publication statusPublished - 2011

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Correlation structure
Stochastic volatility
Stochastic interest rates
Interest rates
Model specification
Pricing
Smile
Assets
Characteristic function
Factors
Option prices
Risk management
Interest rate volatility
Quantitative analysis
Evaluation

Cite this

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title = "Accounting for stochastic interest rates, stochastic volatility and general correlation structure in the valuation of forward starting options",
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 among 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 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. {\circledC} 2010 Wiley Periodicals, Inc.",
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Accounting for stochastic interest rates, stochastic volatility and general correlation structure in the valuation of forward starting options. / van Haastrecht, A.; Pelsser, A.

In: The Journal of Futures Markets, Vol. 31, No. 2, 2011, p. 103-125.

Research output: Contribution to JournalArticleAcademicpeer-review

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AU - Pelsser, A.

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AB - 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 among 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 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. © 2010 Wiley Periodicals, Inc.

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