On martingale measures and pricing for continuous bond-stock market with stochastic bond
Abstract
This paper studies pricing of stock options for the case when the evolution of the risk-free assets or bond is stochastic. We show that, in the typical scenario, the martingale measure is not unique, that there are non-replicable claims, and that the martingale prices can vary significantly; for instance, for a European put option, any positive real number is a martingale price for some martingale measure. In addition, the second moment of the hedging error for a strategy calculated via a given martingale measure can take any arbitrary positive value under some equivalent measure. Some reasonable choices of martingale measures are suggested, including a measure that ensures local risk minimizing hedging strategy.Download Info
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Paper provided by arXiv.org in its series Papers with number 1108.0719.Length:
Date of creation: Aug 2011
Date of revision:
Handle: RePEc:arx:papers:1108.0719
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Web page: http://arxiv.org/
Related research
Keywords:This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-09 (All new papers)
References
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- Cheng, Susan T., 1991. "On the feasibility of arbitrage-based option pricing when stochastic bond price processes are involved," Journal of Economic Theory, Elsevier, vol. 53(1), pages 185-198, February.
- Yong-Jin Kim & Naoto Kunitomo, 1999. "Pricing Options under Stochastic Interest Rates: A New Approach," Asia-Pacific Financial Markets, Springer, vol. 6(1), pages 49-70, January.
- Kerry Back, 2010. "Martingale Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 235-250, December.
- Benninga, Simon & Björk, Tomas & Wiener, Zvi, 2002. "On the Use of Numeraires in Option pricing," Working Paper Series in Economics and Finance 484, Stockholm School of Economics.
- Nikolai Dokuchaev, 2011. "Option Pricing Via Maximization Over Uncertainty And Correction Of Volatility Smile," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 507-524.
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