The Evaluation Of Barrier Option Prices Under Stochastic Volatility
AbstractThis paperc onsiders the problem o fnumerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993). We develop a method of lines approach to evaluate the price as well as the delta and gamma of the option. The method is able to effciently handle bothc ontinuously monitored and discretely monitored barrier options and can also handle barrier options with early exercise features. In the latter case, we can calculate the early exercise boundary of an American barrier option in both the continuously and discretely monitored cases.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 266.
Date of creation: 01 Jan 2010
Date of revision:
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barrier option; stochastic volatility; continuously monitored; discretely monitored; free boundary problem; method of lines; Monte Carlo simulation;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-02-27 (All new papers)
- NEP-BEC-2010-02-27 (Business Economics)
- NEP-ORE-2010-02-27 (Operations Research)
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- Maya Briani & Lucia Caramellino & Antonino Zanette, 2013. "A hybrid tree-finite difference approach for the Heston model," Papers 1307.7178, arXiv.org, revised Oct 2013.
- Susanne Griebsch & Kay Pilz, 2012. "A Stochastic Approach to the Valuation of Barrier Options in Heston's Stochastic Volatility Model," Research Paper Series 309, Quantitative Finance Research Centre, University of Technology, Sydney.
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