We develop highly-efficient parallel Partial Differential Equation (PDE) based pricing methods on Graphics Processing Units (GPUs) for multi-asset American options. Our pricing approach is built upon a combination of a discrete penalty approach for the linear complementarity problem arising due...

We study a parallel implementation on a Graphics Processing Unit (GPU) of Alternating Direction Implicit (ADI) time-discretization methods for solving time-dependent parabolic Partial Differential Equations (PDEs) in three spatial dimensions with mixed spatial derivatives in a variety of...

In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in Gatheral's book and the large-time asymptotic of the Heston implied volatility agree algebraically, thus confirming a conjecture from Gatheral as well as providing a...

We present a Graphics Processing Unit (GPU) parallelization of the computation of the price of exotic cross-currency interest rate derivatives via a Partial Differential Equation (PDE) approach. In particular, we focus on the GPU-based parallel pricing of long-dated foreign exchange (FX)...

In this paper we discuss the Malliavin differentiability of a particular class of Feller diffusions which we call $\delta$-diffusions. This class is given by \begin{equation*} d\nu_t=\kappa(\theta-\nu_t))dt \eta \nu_t^{\delta}d\mathbb W_t^2, \delta\in[\frac{1}{2},1] \end{equation*} and appears...

In this paper we derive the locally risk-minimizing hedging for a general contingent claim in an incomplete market via the generalized Clark-Ocone formula. Using this result in a stochastic volatility model, we study its connection with the hedge obtained via PDE approach. We see these hedging...

If a probability distribution is sufficiently close to a normal distribution, its density can be approximated by a Gram/Charlier Series A expansion. In option pricing, this has been used fit risk-neutral asset price distributions to the implied volatility smile, ensuring an arbitrage-free...

We develop an efficient Monte Carlo method for the valuation of a financial contract with payoff dependent on discretely realized variance. We assume a general model in which asset returns are random shocks modulated by a stochastic volatility process. Realized variance is the sum of squared...

The Libor Market Model (LMM) describes the evolution of a yield curve through equations for a discrete set of forward rates. In the original version, the rate dynamic was log-normal. The rate dynamic has been extended. The main result presented here is a generic approximation that provides an...

Bilateral CVA as currently implement has the counter-intuitive effect of profiting from one's own widening CDS spreads, i.e. increased risk of default, in practice. The unified picture of CVA and liquidity introduced by Morini & Prampolini 2010 has contributed to understanding this. However,...