The Markov Tree model is a discrete-time option pricing model that accounts for short-term memory of the underlying asset. In this work, we compare the empirical performance of the Markov Tree model against that of the Black-Scholes model and Heston's stochastic volatility model. Leveraging a...

Given bid-offer quotes for a set of listed vanilla options, a fundamental need of option market makers is to interpolate and extrapolate the available quotes to a full arbitrage-free surface. We propose a methodology which directly controls the trade-off between smoothness and bid-offer...

The Heston model is one of the most popular stochastic volatility models for Equity and FX modelling. Although it was developed more than fifteen years ago, its understanding is still not complete and many recent publications have addressed deep theoretical and implementation issues. We review...

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 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)...

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...

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...

In this study, we simplified the Black-Scholes formula to a two-input version. This simplified formula presents a one-to-one relationship with one input given that the other input is fixed. With this simplified formula, we created an option-price data grid and showed that the implied volatility...

We study the pricing of options on realized variance in a general class of Log-OU stochastic volatility models. The class includes several important models proposed in the literature. Having as common feature the log-normal law of instantaneous variance, the application of standard...