In a world of persistently low interest rates, investors look for ways to increase yield without
bearing the full volatility and risk of principal loss of the equities market. A great variety of …

This article deals with the computation of the probability, for a GBM (geometric Brownian
motion) process, to hit sequences of one-sided stochastic boundaries defined as GBM …

This paper deals with a subset of lookback options known as cliquet options. The latter lock
in the best underlying asset price over a number of prespecified dates during the option life. …

Double barrier options have been traded for a long time in the markets and they are embedded
in a variety of popular structured products. However, in their standard form, they lack …

In this article, two general results are provided about the multidimensional Black–Scholes
partial differential equation: its fundamental solution is derived, and it is shown how to turn it …

It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts
with complex payoffs involving joint distributions of several extrema. More specifically, …

This article deals with the boundary crossing probability of a geometric Brownian motion (GBM)
process when the boundary itself is a GBM process. An exact formula is obtained for the …

In this article, the multitouch option, also called the n - touch option (or the “baseball” option
when n = 3 ) is analyzed and valued in closed form. This is a kind of barrier option that has …

This paper examines a path-dependent contingent claim called the window double barrier
option, including standard but also more exotic features such as combinations of single and …

This article provides a closed form solution to the telegrapher’s equation with three space
variables defined on a subset of a sphere within two radii, two azimuthal angles and one polar …