Fast strong approximation Monte Carlo schemes for stochastic volatility models
Numerical integration methods for stochastic volatility models in financial markets are discussed. We concentrate on two classes of stochastic volatility models where the volatility is either directly given by a mean-reverting CEV process or as a transformed Ornstein-Uhlenbeck process. For the latter, we introduce a new model based on a simple hyperbolic transformation. Various numerical methods for integrating mean-reverting CEV processes are analysed and compared with respect to positivity preservation and efficiency. Moreover, we develop a simple and robust integration scheme for the two-dimensional system using the strong convergence behaviour as an indicator for the approximation quality. This method, which we refer to as the IJK (137) scheme, is applicable to all types of stochastic volatility models and can be employed as a drop-in replacement for the standard log-Euler procedure.
Volume (Year): 6 (2006)
Issue (Month): 6 ()
|Contact details of provider:|| Web page: http://www.tandfonline.com/RQUF20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/RQUF20|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
- John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005.
"A Theory Of The Term Structure Of Interest Rates,"
World Scientific Book Chapters,
in: Theory Of Valuation, chapter 5, pages 129-164
World Scientific Publishing Co. Pte. Ltd..
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Beckers, Stan, 1980. " The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
- Sandmann, Klaus & Dieter Sondermann, 1997. "Log-Normal Interest Rate Models: Stability and Methodology," Discussion Paper Serie B 398, University of Bonn, Germany.
- Kahl Christian & Schurz Henri, 2006. "Balanced Milstein Methods for Ordinary SDEs," Monte Carlo Methods and Applications, De Gruyter, vol. 12(2), pages 143-170, April.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
- Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
- Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
- Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(04), pages 907-929, November.
- Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
- Tom Doan, "undated". "RATS programs to replicate CKLS(1992) estimation of interest rate models," Statistical Software Components RTZ00035, Boston College Department of Economics.
- Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
- Rainer Schöbel & Jianwei Zhu, 1999. "Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension," Review of Finance, European Finance Association, vol. 3(1), pages 23-46.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
- Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
- Klaus Sandmann & Dieter Sondermann, 1997. "A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 119-125. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:6:y:2006:i:6:p:513-536. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael McNulty)
If references are entirely missing, you can add them using this form.