Contingent Claims in Incomplete Markets: A Case Study
Author(s)
Sure Mataramvura*
Affiliation(s)
Division of Actuarial Science, School of Management Studies, University of Cape Town, Cape Town, South Africa.
Division of Actuarial Science, School of Management Studies, University of Cape Town, Cape Town, South Africa.
ABSTRACT
In this paper, we revisit pricing contingent claims in incomplete markets. While a lot have been done on pricing in incomplete markets, there is still a gap on the categorization of the payoffs. Some contingent claims are attainable while others will not be attainable. We address the question of which contingent claims belong to each group. We also propose a generalization of the equivalent martingale measures used for pricing, a generalization which includes those studied so far. We also provide some examples of how to price in each class and introduce important definitions.
Cite this paper
S. Mataramvura, "Contingent Claims in Incomplete Markets: A Case Study," Journal of Mathematical Finance, Vol. 3 No. 4, 2013, pp. 426-430. doi: 10.4236/jmf.2013.34044.
S. Mataramvura, "Contingent Claims in Incomplete Markets: A Case Study," Journal of Mathematical Finance, Vol. 3 No. 4, 2013, pp. 426-430. doi: 10.4236/jmf.2013.34044.
References
[1] B. Oksendal, “Stochastic Differential Equations,” 6th Edition, Springer-Verlag, Berlin, 2007. [2] M. Schweizer, “On the Minimal Martingale Measure and the Mollmer-Schweizer Decomposition,” Stochastic Analysis and Applications, Vol. 13, No. 5, 1995, pp. 573-599.
http://dx.doi.org/10.1080/07362999508809418 [3] M. Fritelli, “The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets,” Mathematical Finance, Vol. 10, No. 1, 2000, pp. 39-52.
http://dx.doi.org/10.1111/1467-9965.00079 [4] H. U. Gerber and E. S. W. Shi, “Option Pricing by Esscher Transforms,” Transactions of the Society of Actuaries, Vol. 46, 1994, pp. 99-191. [5] M. Jeanblanc, S. Kloppel and Y. Miyahara, “Minimal -Martingale Measures for Exponential Lévy Processes,” The Annals of Applied Probability, Vol. 17, No. 5-6, 2007, pp. 1615-1638.
http://dx.doi.org/10.1214/07-AAP439 [6] S. Mataramvura, P. Dankemlmann and S. W. Mgobhozi, “Completion of Markets by Variation Processes,” Working Paper, 2013.
[1] B. Oksendal, “Stochastic Differential Equations,” 6th Edition, Springer-Verlag, Berlin, 2007. [2] M. Schweizer, “On the Minimal Martingale Measure and the Mollmer-Schweizer Decomposition,” Stochastic Analysis and Applications, Vol. 13, No. 5, 1995, pp. 573-599.
http://dx.doi.org/10.1080/07362999508809418 [3] M. Fritelli, “The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets,” Mathematical Finance, Vol. 10, No. 1, 2000, pp. 39-52.
http://dx.doi.org/10.1111/1467-9965.00079 [4] H. U. Gerber and E. S. W. Shi, “Option Pricing by Esscher Transforms,” Transactions of the Society of Actuaries, Vol. 46, 1994, pp. 99-191. [5] M. Jeanblanc, S. Kloppel and Y. Miyahara, “Minimal -Martingale Measures for Exponential Lévy Processes,” The Annals of Applied Probability, Vol. 17, No. 5-6, 2007, pp. 1615-1638.
http://dx.doi.org/10.1214/07-AAP439 [6] S. Mataramvura, P. Dankemlmann and S. W. Mgobhozi, “Completion of Markets by Variation Processes,” Working Paper, 2013.