We discuss the probabilistic representation of the solutions of the heat equation perturbed by a repulsive point interaction in terms of a perturbation of Brownian motion, via a Feynman–Kac formula involving a local time functional. An application to option pricing is given, interpolating between the extreme cases of classical Black–Scholes options and knockouts having the barrier situated exactly at the exercise price.
A remark on the heat equation with a point perturbation, the Feynman-Kac formula with local time and derivative pricing
Rinaldi F;
2015-01-01
Abstract
We discuss the probabilistic representation of the solutions of the heat equation perturbed by a repulsive point interaction in terms of a perturbation of Brownian motion, via a Feynman–Kac formula involving a local time functional. An application to option pricing is given, interpolating between the extreme cases of classical Black–Scholes options and knockouts having the barrier situated exactly at the exercise price.File in questo prodotto:
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