Bayesian Pricing of the Optimal-Replication Strategy for European Option in the JD(M)J Model
DOI:
https://doi.org/10.12775/DEM.2012.004Keywords
incomplete markets, Bayesian inference, jump-diffusion process, pricing of deriv-ativesAbstract
In incomplete markets replication strategies may not exist and pricing of derivatives is not an easy task. This paper presents an application of Bertsimas, Kogan and Lo’s algorithm of determining an optimal-replication strategy. In the Merton model the likelihood function is a product of a mixture of infinite number of components. In the paper this number is assumed to be equal to a fixed value M+1. To determine the optimal strategy, we should estimate unknown parameters. To this end we resort to Bayesian estimation techniques. The presented methodology is exemplified by an empirical research.
References
Barndorff-Nielsen, O.E., Shephard, N. (2006), Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation, Journal of Financial Econometrics, 4(1), 1–30.
Bernardo, J. M., Smith, A. F. M. (2002), Bayesian theory, Wiley Series in Probability and Statis-tics.
Bertsekas, D. (1995), Dynamic Programming and Optimal Control, Vol. I, Athena Scientific, Belmont, MA.
Bertsimas, D., Kogan L., Lo, A.W. (2001), Hedging Derivative Securities and Incomplete Markets: an ε-Arbitrage Approach, Operations Research, 49(3), 372–397.
Björk, T. (2004), Arbitrage Theory in Continuous Time, Oxford University Press.
Black, F., Scholes, M. (1973), The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, 637–654.
Frühwirth-Schnatter, S. (2006), Finite Mixture and Markov Switching Models, Springer Science + Business Media, LCC.
Gamerman, D., Lopes, H.F. (2006), Markov Chain Monte Carlo. Stochastic Simulation for Bayes-ian Inference, Chapman & Hall/CRC.
Hanson, F.B., Westman, J.J. (2002), Stochastic Analysis of Jump-Diffusions for Financial Log-Return Processes, Stochastic Theory and Control, 280/2002, 169–183.
Kloeden, P.E., Platen, E. (1992), Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin-Heidelberg-New York.
Kostrzewski, M. (2011), Bayesian inference for the jump-diffusion model with M jumps, Working paper: http://home.agh.edu.pl/ kostrzew/BayesianInferenceJDMJ.pdf.
Lamberton, D., Lapeyre, B. (2000), Introduction to Stochastic Calculus Applied to Finance, CHAPMAN & HALL/CRC.
Lin, S-J., Huang, M-T. (2002), Estimating Jump-Diffusion Models Using the MCMC Simulation, National Tsing Hua University Department of Economics NTHU Working Paper Series, Working paper 0215E, October 2002.
Merton, R.C. (1976), Option pricing when underlying stock return rates are discontinuous, Journal of Financial Economics, 3, 141–183.
Newton, M.A., Raftery, A.E. (1994), Approximate Bayesian inference by the weighted likelihood bootstrap (with discussion), Journal of the Royal Statistical Society B, 56(1), 3–48.
Raftery, A. E., Newton, M. A., Satagopan, J. M., Krivitsky, P. N. (2007), Estimating the Inte-grated Likelihood via Posterior Simulation Using the Harmonic Mean Identity, Bayesian Statistics, 8, 1–45.
Schweizer, M. (1992), Variance-Optimal Hedging in Discrete Time, Mathematics of Operations Research, 20, 1–31.
Shreve, S.E. (2004), Stochastic Calculus for Finance II. Continuous-Time Models, Springer Sci-ence+Business Media, Inc.
Yu, B., Mykland, P. (1998), Looking at Markov Samplers Through CUMSUM Path Plots: A Simple Diagnostic Idea, Statistics and Computing, 8, 275–286.
Downloads
Published
How to Cite
Issue
Section
License
The journal provides an Open Access to its content based on the non-exclusive licence Creative Commons (CC BY-ND 4.0).
To enable the publisher to disseminate the author's work to the fullest extent, the author must agrees to the terms and conditions of the License Agreement with Nicolaus Copernicus University.
Stats
Number of views and downloads: 443
Number of citations: 0
