Pricing Discrete Barrier Options Under Stochastic Volatility

• Ben Arous, G., & Laurence, P. (2009). Second order expansion for implied volatility in two factor local stochastic volatility models and applications to the dynamic λ-SABR model (Preprint).

• Baudoin, F. (2009). Stochastic Taylor expansions and heat Kernel asymptotics. Preprint, Department of Mathematics, Purdue University.

• Fink J. (2003) An examination of the effectiveness of static hedging in the presence of stochastic volatility. Journal of Futures Markets 23(9): 859–890

  Article Google Scholar

• Fournié E., Lasry J.-M., Lebuchoux J., Lions P.-L., Touzi N. (1999) Applications of Malliavin calculus to Monte-Carlo methods in finance. Finance Stoch 3(4): 391–412

  Article Google Scholar

• Fusai G., Abrahams D., Sgarra C. (2006) An exact analytical solution for discrete barrier options. Finance Stoch. 10(1): 1–26

  Article Google Scholar

• Gatheral, J., Hsu, E. P., Laurence, P., Ouyang, C., & Wang, T.-H. (2009). Asymptotics of implied volatility in local volatility models. Forthcoming in Mathematical Finance.

• Malliavin P., Thalmaier A. (2006) Stochastic calculus of variations in mathematical finance. Springer, Berlin

  Google Scholar

• Malliavin P. (1997) Stochastic Analysis. Springer, New York

  Google Scholar

• Shiraya, K., Takahashi, A., & Toda, M. (2009). Pricing barrier and average options under stochastic volatility environment. Preprint, CARF-F-176, Graduate School of Economics, University of Tokyo. Forthcoming in "The Journal of Computational Finance".

• Siopacha M., Teichmann J. (2011) Weak and strong Taylor methods for numerical solutions of stochastic differential equations. Quantitative Finance 11(4): 517–528

  Article Google Scholar

• Takahashi A. (1999) An asymptotic expansion approach to pricing contingent claims. Asia-Pacific Financial Markets 6: 115–151

  Article Google Scholar

• Takahashi, A. (2009). On an asymptotic expansion approach to numerical problems in finance. Selected papers on probability and statistics, Series 2 (Vol. 227 pp. 199–217). American Mathematical Society.

• Takahashi, A., Takehara, K., & Toda. M. (2009). Computation in an asymptotic expansion method. Working paper, CARF-F-149, The University of Tokyo.

• Takahashi, A., & Yamada, T. (2009). An asymptotic expansion with push-down of Malliavin weights (Preprint).

• Takahashi A., Yoshida N. (2004) An asymptotic expansion scheme for optimal investment problems. Statistical Inference for Stochastic Processes 7: 153–188

  Article Google Scholar

• Watanabe, S. (1983). Malliavin’s calculus in terms of generalized Wiener functionals. Lecture notes in control and information science (Vol. 49). Berlin: Springer

• Watanabe S. (1984) Lectures on stochastic differential equations and Malliavin calculus. Springer, Berlin

  Google Scholar

Download references