Pricing a European Option in a Black-Scholes Quanto Market When Stock Price is a Semimartingale

DOI: 10.4236/jmf.2015.53025   PDF   HTML   XML   6,073 Downloads   7,148 Views  


We look at the price of the European call option in a quanto market defined on a filtered probability space when the exchange rate is being modeled by the process where Ht is a semimartingale. Precisely we look at an investor in a Sterling market who intends to buy a European call option in a Dollar market. The market consists of a Dollar bond, Sterling bond and and Sterling risky asset. We first of all convert the Sterling assets by using the exchange rate Et and later on derive an integro-differential equation that can be used to calculate the price on the option.

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Offen, E. and Lungu, E. (2015) Pricing a European Option in a Black-Scholes Quanto Market When Stock Price is a Semimartingale. Journal of Mathematical Finance, 5, 286-303. doi: 10.4236/jmf.2015.53025.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Akigirayi, V. and Booth, G. (1988) Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements. Review of Economics and Statistics, 70, 631-637.
[2] Etheridge, A. (2002) A Course in Financial Calculus. Cambridge Press, Cambridge.
[3] Jorion, P. (1988) On Jump Processes in Foreign Exchange and Stock Markets. Review of Financial Studies, 1, 427-445.
[4] Merton, R. (1976) Option Pricing When Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3, 125-144.
[5] Press, J.A. (1967) A Compound Events Model of Security Prices. Journal of Business, 40, 317-335.
[6] Protter, P. (1992) Stochastic Integration and Differential Equations: A New Approach. Springer-Verlag, Berlin.
[7] Shiryaev, A.N. (1999) Essentials of Stochastic Finance, Facts, Models, Theory. World Scientific Pub Co Inc., Hackensack.
[8] Jacod, J. and Shiryaev A.N. (1987) Limit Theorems for Stochastic Processes. Springer, Berlin.
[9] Klebanner, F. (2005) Introduction to Stochastic Calculus with Applications. Imperial College Press, Berlin.
[10] Papapantoleoen, A. (2006) Application for Semimartingales and Lèvy Processes in Finance: Duality and Valuation. Dissertation zur Erlangung des Doktorgrades der Fakultät für Mathematik und Physik der Albert-Ludwigs-Universitat, Freiburg im Breisgau.
[11] Kallesen, J. and Shiryaev, A. (2002) The Cummlant Process and Esscher’s Change of Measure. Finance and Stochastics, 6, 397-428.
[12] Bulhman, H., Delbaen, F., Embrechts, P. and Shiryaev, A.N. (1996) No-Arbitrage, Change of Measure and Conditional Esscher’s Transforms. CW Quartery, 9, 291-317.
[13] Harrison, J. and Pliska, S. (1981) Martingales and Stochastic Integrals in Theory of Continuous Trading. Stochastic Processes and Their Applications, 11, 215-260.
[14] Follmer, H. and Schwaizer, M. (1991) Hedging Contingent Claims under Incomplete Information. In: Davis, M.A. and Elliot, R.J., Eds., Applied Stochastic Analysis Monographs, 4th Edition, Vol. 5, Gordon and Breach, London, 389-414.
[15] Miyahara, Y. (1999) Minimal Entropy Martingale Measures Jump Type Price Process in Incomplete Asset Markets. Asian-Pacific Financial Markets, 6, 97-113.
[16] Vecer, J. (2003) Pricing Asian Options in Semimartingale Model. Columbia University, New York.
[17] Baxter, M. and Rennie, A. (1996) Financial Calculus: An Introduction to Derivative Pricing. Cambridge University Press, Cambridge, England.

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