Unbiased Monte Carlo Methods for Lookback options in Jump-diffusion models
نویسنده
چکیده
In this paper, we present an unbiased Monte Carlo estimator for lookback options in jumpdiffusion models. Lookback options are difficult to price in jump-diffusion models, as their pay-off depends on the maximum of the share price over a particular time interval. In general, closed form solutions for prices of lookback options are not available but even simulating the pay-off of such an option is difficult. We show that after conditioning on jump times, the values of the share price just before and after the jumps and at maturity, we recover a finite number of Brownian bridges. The law of the maximum of a Brownian Bridge is well-known and we show in this paper that it can be simulated from. This realization allows us to derive an unbiased Monte Carlo estimator for lookback options in jump-diffusion models.
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