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

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DOI: 10.4236/jmf.2015.53025    5,591 Downloads   6,400 Views  

ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

[1] Akigirayi, V. and Booth, G. (1988) Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements. Review of Economics and Statistics, 70, 631-637.
http://www.jstor.org/stable/1935826
[2] Etheridge, A. (2002) A Course in Financial Calculus. Cambridge Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511810107
[3] Jorion, P. (1988) On Jump Processes in Foreign Exchange and Stock Markets. Review of Financial Studies, 1, 427-445.
http://dx.doi.org/10.1093/rfs/1.4.427
[4] Merton, R. (1976) Option Pricing When Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3, 125-144.
http://dx.doi.org/10.1016/0304-405X(76)90022-2
[5] Press, J.A. (1967) A Compound Events Model of Security Prices. Journal of Business, 40, 317-335.
http://dx.doi.org/10.1086/294980
[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.
http://dx.doi.org/10.1007/978-3-662-02514-7
[9] Klebanner, F. (2005) Introduction to Stochastic Calculus with Applications. Imperial College Press, Berlin.
http://dx.doi.org/10.1142/p386
[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.
http://dx.doi.org/10.1007/s007800200069
[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.
http://dx.doi.org/10.1016/0304-4149(81)90026-0
[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.
http://dx.doi.org/10.1017/CBO9780511806636

  
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