Pricing Parisian Options Using Laplace Transforms

Pricing Parisian Options

In this work, we propose to price Parisian options using Laplace transforms. Not only, do we compute the Laplace transforms of all the different Parisian options, but we also explain how to invert them numerically. We discuss the accuracy of the numerical inversion and present the evolution of the Greeks through a few graphs.

Pricing double barrier Parisian options using Laplace transforms

In this article, we study a double barrier version of the standard Parisian options. We give closed formulas for the Laplace transforms of their prices with respect to the maturity time. We explain how to invert them numerically and prove a result on the accuracy of the numerical inversion when the function to be recovered is sufficiently smooth. Henceforth, we study the regularity of the Paris...

Brownian Excursions and Parisian Barrier Options: a Note

This paper addresses the Paris barrier options of [CJY] and their valuation using the Laplace transform approach. The notion of the Paris barrier options is extended such that their valuation is possible at any point during their lifespan, and the pertinent Laplace transforms of [CJY] are modified when necessary.

Jump-Diffusion Models for Asset Pricing in Financial Engineering

In this survey we shall focus on the following issues related to jump-diffusion models for asset pricing in financial engineering. (1) The controversy over tailweight of distributions. (2) Identifying a risk-neutral pricing measure by using the rational expectations equilibrium. (3) Using Laplace transforms to pricing options, including European call/put options, path-dependent options, such as...

Pricing Asian options via Fourier and Laplace transforms