Casella, Bruno and Roberts, Gareth O. (2008) Exact Monte Carlo simulation of killed diffusions. Advances in Applied Probability, Vol.40 (No.1). pp. 273-291. ISSN 0001-8678

Preview

PDF WRAP_Casella1_07-26w.pdf - Draft Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (423Kb)

Abstract

We describe and implement a novel methodology for Monte Carlo simulation of one-dimensional killed diffusions. The proposed estimators represent an unbiased and efficient alternative to current Monte Carlo estimators based on discretization methods for the cases when the finite-dimensional distributions of the process are unknown. For barrier option pricing in finance, we design a suitable Monte Carlo algorithm both for the single barrier case and the double barrier case. Results from numerical investigations are in excellent agreement with the theoretical predictions.

Item Type:	Submitted Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Monte Carlo method, Diffusion processes
Journal or Publication Title:	Advances in Applied Probability
Publisher:	Applied Probability Trust
ISSN:	0001-8678
Date:	March 2008
Volume:	Vol.40
Number:	No.1
Number of Pages:	19
Page Range:	pp. 273-291
Identification Number:	10.1239/aap/1208358896
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
References:	Anderson, T. W. (1960). A modification of the sequential probability ratio test to reduce the sample size. Ann. Math. Statist., 31:165–197. Asmussen, S. and Glynn, P. W. (2007). Stochastic Simulation. Algorithms and Analysis. Springer-Verlag, New York. Forthcoming. Bertoin, J. and Pitman, J. (1994). Path transformations connecting Brownian bridge, excursion and meander. Bull. Sci. Math., 118(2):147–166. Beskos, A., Papaspiliopoulos, O., and Roberts, G. O. (2006a). Retrospective exact simulation of diffusion sample paths with applications. Bernoulli, 12(6):1077–1098. Beskos, A., Papaspiliopoulos, O., and Roberts, G. O. (2007). A new factorisation of diffusion measure and sample path reconstruction. Submitted. Beskos, A., Papaspiliopoulos, O., Roberts, G. O., and Fearnhead, P. (2006b). Exact and efficient likelihood based inference for discretely observed diffusions (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol., 68(3):333–382. Beskos, A. and Roberts, G. O. (2005). Exact simulation of diffusions. Ann. Appl. Probab., 15(4):2422–2444. Black, F. and Cox, J. C. (1976). Valuing corporate securities: some effects of bond indenture provisions. Journal of Finance, 31:351–367. Bossy, M., Gobet, E., and Talay, D. (2004). A symmetrized Euler scheme for an efficient approximation of reflected diffusions. J. Appl. Probab., 41(3):877– 889. Davydov, D. and Linetsky, V. (2001). The valuation and hedging of barrier and lookback options under the cev process. Management Science, 47:949–965. Devroye, L. (1986). Nonuniform random variate generation. Springer-Verlag, New York. Doob, J. L. (1949). Heuristic approach to the Kolmogorov-Smirnov theorems. Ann. Math. Statistics, 20:393–403. Fearnhead, P., Papaspiliopoulos, O., and Roberts, G. O. (2006). Particle filters for partially observed diffusions. Submitted. Gobet, E. (2000). Weak approximation of killed diffusion using Euler schemes. Stochastic Process. Appl., 87(2):167–197. Gobet, E. (2001). Euler schemes and half-space approximation for the simulation of diffusion in a domain. ESAIM Probab. Statist., 5:261–297 (electronic). L´epingle, D. (1995). Euler scheme for reflected stochastic differential equations. Math. Comput. Simulation, 38(1-3):119–126. Probabilit´es num´eriques (Paris, 1992). Lerche, H. R. (1986). Boundary crossing of Brownian motion, volume 40 of Lecture Notes in Statistics. Springer-Verlag, Berlin. Its relation to the law of the iterated logarithm and to sequential analysis. Longstaff, F. A. and Schwarz, E. S. (1995). A simple approach to valuing risky and floating rate debt. Journal of Finance, 50:789–819. Merton, R. C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management, (4):141–183. Oksendal, B. K. (1998). Stochastic Differential Equations: An Introduction With Applications. Springer-Verlag. P¨otzelberger, K. and Wang, L. (2001). Boundary crossing probability for Brownian motion. J. Appl. Probab., 38(1):152–164. Reiner, E. and Rubinstein, M. (1991). Breaking down the barriers. Risk, 4(8):28– 35.
URI:	http://wrap.warwick.ac.uk/id/eprint/30043

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item