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State Price Density Estimation and Nonparametric Pricing of Basket Options

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DOI: 10.4236/jmf.2015.55038    4,287 Downloads   4,614 Views  

ABSTRACT

This paper develops a novel method to price basket options by using an application-driven approach to estimating the state price density of the basket or the joint state price density of the asset prices in the basket. In this connection, we also discuss the difference between the application-driven and the traditional statistical approach to density estimation.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Kuang, Y. and Lai, T. (2015) State Price Density Estimation and Nonparametric Pricing of Basket Options. Journal of Mathematical Finance, 5, 448-456. doi: 10.4236/jmf.2015.55038.

References

[1] Caldana, R., Fusai, G., Gnoatto, A. and Grasselli, M. (2014) General Closed-Form Basket Option Pricing Bounds. Available at SSRN 2376134.
[2] Hutchinson, J.M., Lo, A.W. and Poggio, T. (1994) A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks. Journal of Finance, 49, 851-889.
http://dx.doi.org/10.1111/j.1540-6261.1994.tb00081.x
[3] Aït-Sahalia, Y. and Lo, A.W. (1998) Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices. Journal of Finance, 53, 499-547.
http://dx.doi.org/10.1111/0022-1082.215228
[4] Aït-Sahalia, Y. and Duarte, J. (2003) Nonparametric Option Pricing under Shape Restrictions. Journal of Econometrics, 116, 9-47.
http://dx.doi.org/10.1016/S0304-4076(03)00102-7
[5] Härdle, W. and Yatchew, A. (2001) Dynamic Nonparametric State Price Density Estimation Using Constrained Least Squares and the Bootstrap. Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes No. 2002, 16.
[6] Yuan, M. (2009) State Price Density Estimation via Nonparametric Mixtures. Annals of Applied Statistics, 3, 963-984.
http://dx.doi.org/10.1214/09-AOAS246
[7] Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. The Journal of Political Economy, 81, 637-654.
http://dx.doi.org/10.1086/260062
[8] Breeden, D.T. and Litzenberger, R.H. (1978) Prices of State-Contingent Claims Implicit in Option Prices. Journal of Business, 51, 621-651.
http://dx.doi.org/10.1086/296025
[9] Banz, R.W. and Miller, M.H. (1978) Prices for State-Contingent Claims: Some Estimates and Applications. Journal of Business, 51, 653-672.
http://dx.doi.org/10.1086/296026
[10] Ferguson, T.S. (1983) Bayesian Density Estimation by Mixtures of Normal Distributions. Recent Advances in Statistics, 24, 287-302.
[11] Escobar, M.D. and West, M. (1995) Bayesian Density Estimation and Inference Using Mixtures. Journal of the American Statistical Association, 90, 577-588.
http://dx.doi.org/10.1080/01621459.1995.10476550
[12] Kuo, L. (1986) Computations of Mixtures of Dirichlet Processes. SIAM Journal on Scientific and Statistical Computing, 7, 60-71.
http://dx.doi.org/10.1137/0907004
[13] Scott, D.W. and Sain, S.R. (2005) Multidimensional Density Estimation. In: Rao, C.R., Ed., Handbook of Statistics Elvesier, New York, 229-261.
http://dx.doi.org/10.1016/s0169-7161(04)24009-3
[14] Hwang, J.N., Lay, S.R. and Lippman, A. (1994) Nonparametric Multivariate Density Estimation: A Comparative Study. IEEE Transactions on Signal Processing, 42, 2795-2810.
http://dx.doi.org/10.1109/78.324744
[15] Sian, S.R., Baggerly, K.A. and Scott, D.W. (1994) Cross-Validation of Multivariate Densities. Journal of American Statistical Association, 89, 807-817.
http://dx.doi.org/10.1080/01621459.1994.10476814
[16] Duong, T. (2007) ks: Kernel Density Estimation and Kernel Discriminant Analysis for Multivariate Data in R. Journal of Statistical Software, 21, 1-16.
http://dx.doi.org/10.18637/jss.v021.i07

  
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