We calculate several hitting time probabilities for a correlated multidimensional Brownian bridge process, where the boundaries are hyperplanes that move linearly with time. We compute the probability that a Brownian bridge will cross a moving hyperplane if the endpoints of the bridge lie on the...

In this paper we derive analytic formulae for statistical arbitrage trading where the security price follows an Ornstein–Uhlenbeck process. By framing the problem in terms of the first-passage time of the process, we derive expressions for the mean and variance of the trade length and the...

Imposing a symmetry condition on returns, Carr and Lee (Math Financ 19(4):523–560, <CitationRef CitationID="CR10">2009</CitationRef>) show that (double) barrier derivatives can be replicated by a portfolio of European options and can thus be priced using fast Fourier techniques (FFT). We show that prices of barrier derivatives in...</citationref>

We show how to simulate Brownian motion not on a regular time grid, but on a regular spatial grid. That is, when it first hits points in δZ for some δ0. Central to our method is an algorithm for the exact simulation of τ, the first time Brownian motion hits ±1. This work is motivated by...

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, for example, for the pricing of single-barrier and double-barrier options in a Black–Scholes...

We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities...