On the Valuation of Discrete Asian Options in High Volatility Environments

References

• Black F., and Scholes M.. 1973. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81: 637–654.
   Web of Science ®Google Scholar
• Boyle P., and Potapchik A.. 2008. “Prices and Sensitivities of Asian Options: A Survey.” Insurance: Mathematics and Economics 42: 189–211.
   Web of Science ®Google Scholar
• Carr P., Ewald C.-O., and Xiao Y.. 2008. “On the Qualitative Effect of Volatility and Duration on Prices of Asian Options.” Finance Research Letters 5: 162–171.
   Web of Science ®Google Scholar
• Cox J. C., Ingersoll J., Jonathan E., and Ross S. A.. 1985. “A Theory of the Term Structure of Interest Rates.” Econometrica 53 (2): 385–407.
   Web of Science ®Google Scholar
• Delbaen F., and Schachermayer W.. 2006. The Mathematics of Arbitrage. Berlin: Springer Finance.
   Google Scholar
• Desmettre S., Leobacher G., and Rogers L. C. G.. 2021. “Change of Drift in One-dimensional Diffusions.” Finance and Stochastics 25 (2): 359–381.
   Web of Science ®Google Scholar
• Geman H., and Yor M.. 1993. “Bessel Processes, Asian Options, and Perpetuities.” Mathematical Finance 3 (4): 349–375.
   Google Scholar
• Gronwall T. H. 1919. “Note on the Derivative with Respect to a Parameter of the Solutions of a System of Differential Equations.” Annals of Mathematics 20: 292–296.
   Google Scholar
• Guliashvili A., and Stein E. M.. 2010. “Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models.” Applied Mathematics and Optimization 61: 287–315.
   Web of Science ®Google Scholar
• Hambly B., and Kolliopoulus N.. 2019. “Stochastic Evolution Equations for Large Portfolios of Stochastic Volatility Models.” https://arxiv.org/abs/1701.05640.
   Google Scholar
• Heston S. L. 1993. “A Closed-form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” The Review of Financial Studies 6 (2): 327–343.
   Web of Science ®Google Scholar
• Jacquier A., Keller-Ressel M., and Mijatović A.. 2013. “Large Deviations and Stochastic Volatility Models with Jumps: Asymptotic Implied Volatility for Affine Models.” Stochastics 85 (2): 321–345.
   Google Scholar
• Jacquier A., and Mijatović A.. 2014. “Large Deviations for the Extended Heston Model: The Large-time Case.” Asia-Pacific Financial Markets 21: 263–280.
   Google Scholar
• Jessen B. 1933. “Om Uligheder Imellem PotensmiddelvæRdier.” Matematisk Tidsskrift B: 1–19.
   Google Scholar
• Kamizono K., Kariya T., Liu R. Y., and Nakatsuma T.. 2004. “A New Control Variate Estimator for An Asian Option.” Asia-Pacific Financial Markets 11: 143–160.
   Google Scholar
• Karatzas I., and Shreve S. E.. 1991. Brownian Motion and Stochastic Calculus. 2nd ed. Vol. 113 of Graduate Texts in Mathematics. New York: Springer-Verlag.
   Google Scholar
• Kemna A. G. Z., and Vorst A. C. F.. 1990. “A Pricing Method for Options Based on Average Asset Values.” Journal of Banking and Finance 14: 113–129.
   Web of Science ®Google Scholar
• Kim B., and Wee I.-S.. 2014. “Pricing of Geometric Asian Options Under Heston's Stochastic Volatility Model.” Quantitative Finance 14 (10): 1795–1809.
   Web of Science ®Google Scholar
• Korn R., Korn E., and Kroisandt G.. 2010. Monte Carlo Methods and Models in Finance and Insurance. Boca Raton: Chapman & Hall/CRC.
   Google Scholar
• Kraft H. 2005. “Optimal Portfolios and Heston's Stochastic Volatility Model: An Explicit Solution for Power Utility.” Quantitative Finance 5 (3): 303–313.
   Web of Science ®Google Scholar
• Mendonca K., Kontosakos V. E., Pantelous A. A., and Zuev K. M.. 2018. “Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation.” https://arxiv.org/abs/1803.03364.
   Google Scholar
• Shiryaev A. 1996. Probability. 2nd ed. New York, NY: Springer.
   Google Scholar
• Vecer J. 2001. “A New PDE Approach for Pricing Arithmetic Average Asian Options.” Journal of Computational Finance 4 (4): 105–113.
   Google Scholar
• Wong B., and Heyde C.. 2006. “On Changes of Measure in Stochastic Volatility Models.” Journal of Applied Mathematics and Stochastic Analysis 2006: 1–13.
   Google Scholar
• Zhan H., and Cheng Q.. 2004. “A New Multiple Control Variate Estimator for Asian Options.” Acta Scientarium Naturalium Universitatis Pekinensis 40 (1): 5–11.
   Google Scholar
• Zhang P. 1998. Exotic Options. 2nd ed. Singapore: World Scientific Publishing Co Pte Ltd.
   Google Scholar