We apply adjoint algorithmic differentiation (AAD) to the risk management of derivative securities in the situation where the dynamics of securities prices are given in terms of partial differential equations (PDE). With simple examples, we show how AAD can be applied to both forward and...

We present an accurate and easy-to-compute approximation of the transition probabilities and the associated Arrow-Debreu (AD) prices for the Inhomogeneous Geometric Brownian Motion (IGBM) model for interest rates, default intensities or volatilities. Through this procedure, dubbed exponent...

We investigate the joint distribution and the multivariate survival functions for the maxima of an Ornstein-Uhlenbeck (OU) process in consecutive time-intervals. A PDE method, alongside an eigenfunction expansion, is adopted with which we first calculate the distribution and the survival...

This thesis concentrates on FVA computation for interest rate swaps under perfect collateralization and re-hypothecation. It also analyses the effect of FVA computation in a portfolio level. With a Hull-White set-up for interest rate, we are able to compute FVA for single swap and swap...

We present an accurate and easy-to-compute approximation of zero-coupon bonds and Arrow-Debreu (AD) prices for the Black-Karasinski model of interest rates or default intensities. Through this procedure, dubbed exponent expansion, AD prices are obtained as a power series in time to maturity....

We show how Algorithmic Differentiation can be used to implement efficiently the Pathwise Derivative method for the calculation of option sensitivities with Monte Carlo. The main practical difficulty of the Pathwise Derivative method is that it requires the differentiation of the payout...

In this paper we propose a novel, analytically tractable, one-factor stochastic model for the dynamics of credit default swap (CDS) spreads and their returns, which we refer to as the spread-return mean-reverting (SRMR) model. The SRMR model can be seen as a hybrid of the Black-Karasinski model...