A new option pricing formula is presented that unifies several results of the existing literature on exotic option pricing under Lèvy processes and generates new valuation formulas within the Lévy framework. To demonstrate the flexibility of the method a few examples are given and the known...

I address the dichotomy between American put option pricing theory and the numerical algorithms designed to estimate American put option prices. The literature has focused only on pricing error. However, early exercise is the essence of American option pricing (exercising) and with it comes the...

Stochastic volatility option pricing has become popular in financial mathematics due to its theoretical and empirical consistencies. However, stochastic volatility models generally suffer from analytical and calibration intractability, except for regime switching stochastic volatility. However,...

In a discrete time option pricing framework, we compare the empirical performance of two pricing methodologies, namely the affine stochastic discount factor (SDF) and the empirical martingale correction methodologies. Using a CAC 40 options dataset, the differences are found to be small: the...

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. The data set is the daily log returns of the French CAC40 index, on the period January 2, 1988, October 26, 2007. Under...

In a discrete time option pricing framework, we compare the empirical performance of two pricing methodologies, namely the affine stochastic discount factor and the empirical martingale correction methodologies. Using a CAC 40 options dataset, the differences are found to be small : the higher...

Volatility has a significant role to play in the determination of risk and in the valuation of options and other financial derivatives. The well-known Black-Scholes model for the financial derivatives deals with constant volatility. This paper presents a new model based on shot noise behaviour,...

We discuss the accurate numerical solution of Black-Scholes differential equations. We check that the stochastic part of the equation could convert small round-off or truncation errors in big errors. However, the numerical method used are low order even in the non-stochastic case due to the...