The aim of this paper is to obtain the valuation formulas for European and barrier options if the underlying of the option contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. The paper is build upon the framework developed in Necula (2007) for...

The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan (1998), extends to "standard dispersion" options written on the Euclidean norm of a vector of n asset performances. With the help of...

We price derivatives defined for different asset classes with a full stochastic dependence structure. We consider jointly geometric Brownian motions and mean-reversion processes with a a stochastic variance-covariance matrix driven by a Wishart process. These models cannot be treated within the...

In this paper, we present a new precipitation model based on a multi-factor Ornstein-Uhlenbeck approach of pure-jump type. In this setup, we derive a representation for the related precipitation swap price process and infer its risk-neutral time dynamics. We further deduce a pricing formula for...

The investment industry lacks an unified framework for handling derivative instruments in general portfolio management. With the increased use of derivatives, there is a need for a framework that aligns fundamental terminology and concepts. The main challenges with the current practices are...

In this paper, we derive optimal hedging strategies for options in electricity futures markets. Optimality is measured in terms of minimal variance and the associated minimal variance hedging portfolios are obtained by a stochastic maximum principle. Our explicit results are particularly useful...

We extend the arithmetic multi-factor electricity spot price model proposed by Benth, Kallsen & Meyer-Brandis by adding stochastic mean-level processes to their model and by taking additional information on the future behavior of these mean-level processes into account. The available...

Given the inherent complexity of financial markets, a wide area of research in the field of mathematical finance is devoted to develop accurate models for the pricing of contingent claims. Focusing on the stochastic volatility approach (i.e. we assume to describe asset volatility as an...

This paper discusses how to obtain the Black-Scholes equation to evaluate options and how to obtain explicit solutions for Call and Put. The Black-Scholes equation, which is the basis for determining explicit solutions for Call and Put, is a rather sophisticated equation. It is a partial...