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Original Articles

Stochastic Correlation and Volatility Mean-reversion – Empirical Motivation and Derivatives Pricing via Perturbation Theory

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Pages 555-594 | Received 05 Sep 2012, Accepted 10 Feb 2014, Published online: 14 Apr 2014

References

  • Alexander, C. (2000). A primer on the orthogonal GARCH model. Manuscript ISMA Centre, University of Reading, Berkshire.
  • Alexander, C. (2001). Orthogonal GARCH. Mastering Risk, 2, 21–38.
  • Andersen, T. G., Bollerslev, T., Diebold, F. X., & Ebens, H. (2001). The distribution of realized stock return volatility. Journal of Financial Economics, 61, 43–76. doi:10.1016/S0304-405X(01)00055-1
  • Ball, C., & Roma, A. (1994). Stochastic volatility option pricing. The Journal of Financial and Quantitative Analysis, 29, 589–607. doi:10.2307/2331111
  • Ball, C. A., & Torous, W. N. (2000). Stochastic correlation across international stock markets. Journal of Empirical Finance, 7, 373–388. doi:10.1016/S0927-5398(00)00017-7
  • da Fonseca, J., Grasselli, M., & Tebaldi, C. (2007). Option pricing when correlations are stochastic: An analytical framework. Review of Derivatives Research, 10, 151–180. doi:10.1007/s11147-008-9018-x
  • Deelstra, G., & Parker, G. (1995). A covariance equivalent discretisation of the CIR model. Proceedings of the 5th AFIR International Colloquium, 2, 731–747.
  • Drǎgulescu, A. A., & Yakovenko, V. M. (2002). Probability distribution of returns in the Heston model with stochastic volatility. Quantitative Finance, 2, 443–453. doi:10.1080/14697688.2002.0000011
  • Engle, R., & Patton A. J. (2001). What good is a volatility model? Quantitative Finance, 1, 237–245. doi:10.1088/1469-7688/1/2/305
  • Escobar, M., Gotz, B., Seco, L., & Zagst R. (2010). Pricing a CDO on stochastically correlated underlyings. Quantitative Finance, 10, 265–277. doi:10.1080/14697680802629418
  • Escobar, M., & Olivares, P. (2013). Pricing of mountain range derivatives under a principal component stochastic volatility model. Applied Stochastic Models in Business and Industry, 29(1), 31–44.
  • Fouque, J., Garnier, J., Papanicolaou, G., & Solna, K. (2007). Wave propagation and time reversal in randomly layered media (1st ed.). New York, NY: Springer.
  • Fouque, J., & Han, C. (2003). Pricing Asian options with stochastic volatility. Quantitative Finance, 3, 353–362. doi:10.1088/1469-7688/3/5/301
  • Fouque, J. P., Papanicolaou, G., & Sircar, K. R. (1999). Financial modeling in a fast mean-reverting stochastic volatility environment. Asia-Pacific Financial Markets, 6, 37–48.
  • Fouque, J., Papanicolaou, G., & Sircar, R. (2000). Derivatives in financial markets with stochastic volatility (1st ed.). River Edge, NJ: Cambridge University Press.
  • Fouque, J., Papanicolaou, G., Sircar, R., & Solna, K. (2003a). Multiscale stochastic volatility asymptotics. SIAM Journal on Multiscale Modeling and Simulation, 2, 22–42. doi:10.1137/030600291
  • Fouque, J., Papanicolaou, G., Sircar, R., & Solna, K. (2003b). Short time-scales in S&P 500 volatility. Journal of Computational Finance, 6, 1–23.
  • Fouque, J., Papanicolaou, G., Sircar, R., & Solna, K. (2011). Multiscale Stochastic volatility for equity, interest-rate and credit derivatives (1st ed.). New York, NY: Cambridge University Press.
  • Fouque, J., Sircar, R., & Solna, K. (2006). Stochastic volatility effects on defaultable bonds. Applied Mathematical Finance, 13, 215–244. doi:10.1080/13504860600563127
  • Fouque, J., Wignall, B., & Zhou, X. (2008). Modeling correlated defaults: First passage model under stochastic volatility. Journal of Computational Finance, 11, 43–78.
  • Gourieroux, C., Jasiak, J., & Sufana, R. (2009). The Wishart autoregressive process of multivariate stochastic volatility. Journal of Econometrics, 150, 167–181. doi:10.1016/j.jeconom.2008.12.016
  • Heath, D., & Schweizer, M. (2000). Martingales versus PDEs in finance: An equivalence result with examples. Journal of Applied Probability, 37, 947–957. doi:10.1239/jap/1014843075
  • Heston, S. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Journal of Finance, 42, 327–343.
  • Howison, S. (2005). Matched asymptotic expansions in Financial engineering. Journal of Engineering Mathematics, 53, 385–406. doi:10.1007/s10665-005-7716-z
  • Hull, J. C., & White, A. D. (1988). An analysis of the bias in option pricing caused by a stochastic volatility. Advances in Options and Futures Research, 3, 29–61.
  • Ilhan, A., Jonsson, M., & Sircar, R. (2004). Singular perturbations for boundary value problems arising from exotic options. SIAM Journal on Applied Mathematics, 64, 1268–1293. doi:10.1137/S0036139902420043
  • Karatzas, I., & Shreve, S. E. (1988). Brownian motion and stochastic calculus (1st ed.). New York, NY: Springer-Verlag.
  • Muhle-Karbe, J., Pfaffel, O., & Stelzer, R. (2012). Option pricing in multivariate stochastic volatility models of OU type. SIAM Journal on Financial Mathematics, 3, 66–94. doi:10.1137/100803687
  • Neykova, D. (2011) Derivatives pricing under stochastic covariance with a fast and a slow mean-reverting component (Diploma Thesis). Technical University of Munich, Munich.
  • Papanicolaou, G., Fouque, J. P., Solna, K., & Sircar, R. (2003). Singular perturbations in option pricing. SIAM Journal on Applied Mathematics, 63, 1648–1665. doi:10.1137/S0036139902401550
  • Philipov, A., & Glickman, M. E. (2006). Multivariate stochastic volatility via Wishart processes. Journal of Business and Economic Statistics, 24, 313–328. doi:10.1198/073500105000000306
  • Pigorsch, C., & Stelzer, R. (2009). A multivariate Ornstein-Uhlenbeck type stochastic volatility model (pp. 1–34). Manuscript submitted for publication.
  • Rasmussen, H., & Wilmott, P. (2002). Asymptotic analysis of stochastic volatility models. In P. Wilmott & H. O. Rasmussen (Eds.), New directions in mathematical finance. Chichester: Wiley.
  • Reed, M., & Barry, S. (1980). Functional analysis (Vol. I, 1st ed.). San Diego, CA: Academic Press.
  • Scott, L. (1987). Option pricing when the variance changes randomly: Theory, estimation and an application. The Journal of Financial and Quantitative Analysis, 22, 419–438. doi:10.2307/2330793
  • Skintzi, V., & Refenes, A. P. (2005). Implied correlation index: A new measure of diversification. Journal of Futures Markets, 25, 171–197. doi:10.1002/fut.20137
  • Stein, E. M., & Stein, J. C. (1991). Stock price distributions with stochastic volatility: An analytic approach. The Review of Financial Studies, 4, 727–752. doi:10.1093/rfs/4.4.727
  • Zauderer, E. (2006). Partial differential equations of applied mathematics. New York, NY: John Wiley & Sons.

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