Log-normal process and martingale restriction bring some bias on the premium for option pricing models. It is possible to reduce the bias by adding more parameters like jump diffusion, stochastic volatility or regime switching. In this case closed form solutions and numerical approximations...

Basket options are among the most popular products of the new generation of exotic options. This attraction is explained by the fact that they can efficiently and simultaneously hedge a wide variety of intrinsically different financial risks. They are flexible enough to include all the risks...

We discuss the efficiency of the spectral method for computing the value of the European Call Options, which is based upon the Fourier series expansion. We propose a simple approach for computing accurate estimates. We consider the general case, in which the volatility is time dependent, but it...

In this paper, we address the mathematical analysis and numerical solution of a model for pricing a defined benefit pension plan. More precisely, the benefits received by the member of the plan depend on the average salary and early retirement is allowed. Thus, the mathematical model is posed as...

Price movements in many commodity markets exhibit significant seasonal patterns. In this paper, we study the effects of seasonal volatility on models’ option pricing performance. In terms of options pricing, a deterministic seasonal component at the price level can be neglected. In contrast,...

Many commodity markets contain a strong seasonal component in volatility. In this paper, the importance of this seasonal behavior for the pricing of commodity options is analyzed. We propose a stochastic volatility model where the drift term of the variance process captures the observed seasonal...

In this paper, we propose a new type of derivative called a pattern derivative. In the simple case of an asset that moves up u or down d in value, a pattern is a sequence of {u, d} movements that may occur before expiration. We provide general pricing formulas that rely on a brute force approach...

We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances. We give a comprehensive...

This research article provides criticism and arguments why the canonical framework for derivatives pricing is incomplete and why the delta-hedging approach is not appropriate. An argument is put forward, based on the efficient market hypothesis, why a proper risk-adjusted discount rate should...