On martingale measures and pricing for continuous bond-stock market with stochastic bond
AbstractThis paper studies stock options pricing in the presence of the stochastic deviations in bond prices. The martingale measure is not unique for this market, and there are non-replicable claims. It is shown that arbitrarily small deviations cause significant changes in the market properties. In particular, the martingale prices and the second moment of the hedging error can vary significantly and take extreme values, for some extreme choices of the martingale measures. The paper suggests ad discusses some choices of the martingale measures.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1108.0719.
Date of creation: Aug 2011
Date of revision: May 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-09 (All new papers)
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- 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.
- 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.
- 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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