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 Itô calculus. This strategy is investigated for vanilla options, barrier options and American options with stochastic volatilities and jumps optionally.
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In honor of the scientific heritage of Jacques-Louis Lions
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Lipp, T., Loeper, G. & Pironneau, O. Mixing monte-carlo and partial differential equations for pricing options. Chin. Ann. Math. Ser. B 34, 255–276 (2013). https://doi.org/10.1007/s11401-013-0763-2
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DOI: https://doi.org/10.1007/s11401-013-0763-2