Paper Infomation
Indifference Pricing in the Single Period Binomial with Complete Market Model
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Author: Jinyang Sun, Yunfei Guo
Abstract: Binomial no-arbitrage price have a method is the traditional approach for derivative pricing, which is, the complete model, which makes possible the perfect replication in the market. Risk neutral pricing is an appropriate method of asset pricing in a complete market. We have discussed an incomplete market, a non - transaction asset that produces incompleteness of the market. An effective method of asset pricing in incomplete markets is the undifferentiated pricing method. This technique was firstly introduced by Bernoulli in (1738) the sense of gambling, lottery and their expected return. It is used to command investors' preferences and better returns the results they expect. In addition, we also discuss the utility function, which is the core element of the undifferentiated pricing. We also studied some important behavior preferences of agents, and injected exponential effect of risk aversion in the model, so that the model was nonlinear in the process of claim settlement.
Keywords: Complete Market Model, Option Pricing, Nonlinear Pricing Formula, Risk Natural Measure, Expected Utility and Indifference Pricing
References:
[1] FASB (2004). Share-based payment (Report). Financial Accounting Standards Board.
[2] Shao Muo Weisi, Zhang Tong, Predictive text mining foundation, Xi'an, Xi'an Jiaotong University Press, 2012.
[3] William Falloon; David Turner, eds. (1999). “The evolution of a market”. Managing Energy Price Risk. London: Risk Books
[4] Kemna, A.G.Z. Vorst, A.C.F.; Rotterdam, E.U.; Instituut, Econometrisch (1990), A Pricing Method for Options Based on Average Asset Values
[5] Feynman R.P., Kleinert H. (1986), ”Effective classical partition functions”, Physical Review A 34: 5080-5084, Bibcode:1986PhRvA..34.5080F, doi:10.1103/PhysRevA.34.5080, PMID 9897894
[6] Devreese J.P.A., Lemmens D., Tempere J. (2010), “Path integral approach to Asianoptions in the Black-Scholes model”，Physica A 389: 780 -788, arXiv:0906.4456, Bibcode:2010PhyA..389..780D, doi:10.1016/j.physa.2009.10.020
[7] Rogers, L.C.G.; Shi, Z. (1995), “The value of an Asian option”, Journal of Applied Probability (Applied Probability Trust) 32 (4): 1077 - 1088, doi: 10.2307/3215221, JSTOR 3215221
[8] V.Henderson and D.Hobson. Utility Indifference pricing: An overview in “Indifference pricing: Theory and Applications” Edited by R.Carmona, Princeton University Press, 2009, pp. 44 - 77
[9] Broadie, M., Glasserman, P., and Kou, S.G. (1997). A continuity correction for discrete barrier options. Mathematical Finance, 7(4), 325 - 348.
[10] Fusai, G., and Roncoroni, A. (2008). Implementing Models in Quantitative Finance: Methods and Cases. Spring-Verlag.
[11] Geman, H., and Yor, M. (1996). Pricing and hedging double-barrier options: A probabilistic approach. Mathematical Finance, 6, 365 - 378.
[12] Heynen, R.C., and Kat, H.M. (1994). Partial barrier options. Journal of Financial Engineering, 3, 253 - 274
[13] Hull, J.C. Options, Futures, and Other Derivative Securities, 3rd edn. Prentice Hall, Engine wood Cliffs, NJ.
[14] Merton, R.C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141 - 183.
[15] Young, D.M., and Gregory, R. T. (1972). A survey of Numerical Mathematics, Volumel. Addison-Wesley.