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Pricing and Hedging Long-Term Options

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  • Hyungbin Park

Abstract

In this article, we investigate the behavior of long-term options. In many cases, option prices follow an exponential decay (or growth) rate for further maturity dates. We determine under what conditions option prices are characterized by this property. To see this, we use the martingale extraction method through which a pricing operator is transformed into a semigroup operator, which is easier to address. We also explore notions of hedging long-term options. Hedging is an attempt to reduce market risks, and we investigate the price sensitivities (Greeks) with respect to such risks, which are typically repre- sented by variations in the underlying process of an option. We combine the Malliavin calculus with the martingale extraction method to analyze Greeks. We see that the ratios between Greeks and the option price are expressed in a simple form in the long term.

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  • Hyungbin Park, 2014. "Pricing and Hedging Long-Term Options," Papers 1410.8160, arXiv.org, revised Mar 2016.
    • Handle: RePEc:arx:papers:1410.8160
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    References listed on IDEAS

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    1. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    2. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    3. Lars Peter Hansen, 2012. "Dynamic Valuation Decomposition Within Stochastic Economies," Econometrica, Econometric Society, vol. 80(3), pages 911-967, May.
    4. Vadim Linetsky, 2004. "The Spectral Decomposition Of The Option Value," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 337-384.
    5. Dmitry Davydov & Vadim Linetsky, 2003. "Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach," Operations Research, INFORMS, vol. 51(2), pages 185-209, April.
    6. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78, January.
    7. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    8. Lars Hansen & José Scheinkman, 2012. "Pricing growth-rate risk," Finance and Stochastics, Springer, vol. 16(1), pages 1-15, January.
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    Cited by:

    1. Hyungbin Park, 2015. "The Martin Integral Representation of Markovian Pricing Kernels," Papers 1504.00276, arXiv.org.
    2. Han, Jihun & Park, Hyungbin, 2015. "The intrinsic bounds on the risk premium of Markovian pricing kernels," Finance Research Letters, Elsevier, vol. 13(C), pages 36-44.

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