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| Mixing Monte-Carlo and Partial Differential Equations for Pricing Options |
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Citation： |
Tobias LIPP,Gr´egoire LOEPER,Olivier PIRONNEAU.Mixing Monte-Carlo and Partial Differential Equations for Pricing Options[J].Chinese Annals of Mathematics B,2013,34(2):255~276 |
| Page view： 3384
Net amount： 3337 |
Authors： |
Tobias LIPP; Gr′egoire LOEPER; Olivier PIRONNEAU; |
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| Abstract： |
There is a need for very fast option pricers when the financial objects are modeled by complex systems of stochastic differential equations. Here the authors investigate option pricers based on mixed Monte-Carlo partial differential solvers for stochastic volatility models such as Heston's. It is found that orders of magnitude in speed are gained on full Monte-Carlo algorithms by solving all equations but one by a Monte-Carlo method, and pricing the underlying asset by a partial differential equation with random coefficients, derived by It\^{o} calculus. This strategy is investigated for vanilla options, barrier options and American options with stochastic volatilities and jumps optionally. |
Keywords： |
Monte-Carlo, Partial differential equations, Heston model, Financial mathematics, Option pricing |
Classification： |
91B28, 65L60, 82B31 |
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