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option pricing; European option; partial information; backward stochastic differential equation
We consider a European option pricing problem under a partial information market, i.e., only the security's price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering technique to solve a utility maximization problem under partial information through transforming the problem under partial information into the classical problem.
[1] Ballestra, L. V., Pacelli, G.: The constant elasticity of variance model: calibration, test and evidence from the Italian equity market. Applied Financial Economics 21 (2011), 1479-1487. DOI 10.1080/09603107.2011.579058
[2] Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Political Econ. 81 (1973), 637-654. DOI 10.1086/260062 | Zbl 1092.91524
[3] Cox, J.: Notes on option pricing I: Constant elasticity of variance diffusions. Working paper, Stanford University (1975) {}
[4] Cox, J. C., Ross, S. A.: The valuation of options for alternative stochastic processes. Journal of Financial Economics 3 (1976), 145-166. DOI 10.1016/0304-405X(76)90023-4
[5] Duffie, D.: Security Markets. Stochastic Models. Economic Theory, Econometrics, and Mathematical Economics Academic Press, Boston (1988). MR 0955269 | Zbl 0661.90001
[6] Karoui, N. El, Peng, S., Quenez, M. C.: Backward stochastic differential equations in finance. Math. Finance 7 (1997), 1-71. DOI 10.1111/1467-9965.00022 | MR 1434407 | Zbl 0884.90035
[7] Emanuel, D. C., MacBeth, J. D.: Further results on the constant elasticity of variance call option pricing model. J. Financial Quant. Anal. 17 (1982), 533-554. DOI 10.2307/2330906
[8] Karatzas, I., Shreve, S. E.: Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics 113 Springer, New York (1988). DOI 10.1007/978-1-4684-0302-2_2 | MR 0917065 | Zbl 0638.60065
[9] Karatzas, I., Shreve, S. E.: Methods of Mathematical Finance. Applications of Mathematics 39 Springer, Berlin (1998). MR 1640352 | Zbl 0941.91032
[10] Lakner, P.: Utility maximization with partial information. Stochastic Processes Appl. 56 (1995), 247-273. DOI 10.1016/0304-4149(94)00073-3 | MR 1325222 | Zbl 0834.90022
[11] Lakner, P.: Optimal trading strategy for an investor: the case of partial information. Stochastic Processes Appl. 76 (1998), 77-97. DOI 10.1016/S0304-4149(98)00032-5 | MR 1637952 | Zbl 0934.91021
[12] Liptser, R. S., Shiryayev, A. N.: Statistics of Random Processes. I. General Theory. Applications of Mathematics 5 Springer, New York (1977). MR 0474486 | Zbl 0364.60004
[13] Liptser, R. S., Shiryayev, A. N.: Statistics of Random Processes. II. Applications. Applications of Mathematics 6 Springer, New York (1978). MR 0488267 | Zbl 0369.60001
[14] Ma, J., Yong, J.: Forward-Backward Stochastic Differential Equations and Their Applications. Lecture Notes in Mathematics 1702 Springer, Berlin (1999). MR 1704232 | Zbl 0927.60004
[15] Merton, R. C.: Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4 (1973), 141-183. DOI 10.2307/3003143 | MR 0496534
[16] Merton, R. C.: Continuous-Time Finance. Blackwell, Cambridge (1999). Zbl 1019.91502
[17] Øksendal, B.: Stochastic Differential Equations. An Introduction with Applications. Universitext Springer, Berlin (1998). Zbl 0897.60056
[18] Wu, Z., Wang, G. C.: A Black-Scholes formula for option pricing with dividends and optimal investment problems under partial information. J. Syst. Sci. Math. Sci. 27 Chinese (2007), 676-683. MR 2375534 | Zbl 1150.91397
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