Vibrato Monte Carlo sensitivities.
We show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the Likelihood Ratio Method. With a variance reduction modification, this results in an estimator which f...
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| Format: | Working paper |
| Language: | English |
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Oxford-Man Institute of Quantitative Finance
2007
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| Summary: | We show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the Likelihood Ratio Method. With a variance reduction modification, this results in an estimator which for timestep h has a variance which is O(h−1/2) for discontinuous payoffs and O(1) for continuous payoffs. Numerical results confirm the variance is much lower than the O(h−1) variance of the Likelihood Ratio Method, and the approach is also compatible with the use of adjoints to obtain multiple first order sensitivities at a fixed cost. |
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