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 usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth. Using Itô's formula, we get rid, in the asset price...

In this paper, we study financial markets with stochastic volatilities driven by fractional Brownian motion with Hurst index H1/2. Our models include fractional versions of Ornstein-Uhlenbeck, Vasicek, geometric Brownian motion and continuous-time GARCH models. We price variance and volatility...

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...

The valuation of the variance swaps for local Levy based stochastic volatility with delay (LLBSVD) is discussed in this paper. We provide some analytical closed forms for the expectation of the realized variance for the LLBSVD. As applications of our analytical solutions, we fit our model to 10...

In this paper we discuss the pricing of Constant Maturity Credit Default Swaps (CMCDS) under single sided jump models. The CMCDS offers default protection in exchange for a floating premium which is periodically reset and indexed to the market spread on a CDS with constant maturity tenor written...

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 develop a lattice method for pricing lookback options in a regime-switching market environment. We assume the market is governed by a two-state Markov chain and stock volatility can change whenever the market environment changes. We develop a method which resolves the bias in the binomial...

In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model, by developing efficient transform based pricing methods. This non-affine model gives prices of options on realized variance which allow upward sloping implied...

We present a new numerical method to price vanilla options in time-changed Brownian motion models quickly. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a number of widely used models. In particular, we use the...