Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Due to the discontinuous payoff of barrier options, finite difference methods typically lead to large error for the price function and spatial derivatives near expiry date and the barrier. Furthermore, usual Monte-Carlo estimators for their price and sensitivities typically have significant variance. In this work, we consider alternative representations for barrier option prices in terms of 3-dimensional Bessel processes and bridges, and show how this leads to better estimators, especially for short maturities where we are able to increase the estimator efficiency dramatically.

We also discuss the related problem of efficient estimation of the density (and not just cumulative distribution function) of first-passage times for diffusions. Even though the density estimation problem is essentially non-parametric, our method achieves (the typical Monte-Carlo) square-root order of convergence. (joint with Tomoyuki Ichiba, Columbia University) ( slides)

Speaker: Kostas Kardaras, Boston University