Since the seminar work by Black and Sholes on option pricing early 1970’s, many alternative option pricing models have appeared to address some key stylized facts for option markets such as volatility smile, fat-tail, volatility clustering, and so on. Most of the successful option models are parametric models based on diffusion processes with jumps usually called the Lévy processes and the para...

The numerical solution of several mathematical models arising in financial economics for the valuation of both European and American call options on different types of assets is considered. All the models are based on the Black-Scholes partial differential equation. In the case of European options a numerical upwind scheme for solving the boundary backward parabolic partial differential equatio...

and Applied Analysis 3 For the sake of clarity in the presentation we recall that in a jump-diffusion model, the modified stochastic differential equation SDE for the underlying asset is dS S μdt σdz ( η − 1dq, 1.1 where S is the underlying stock price, μ is the drift rate, σ is the volatility, dz is the increment of Gauss-Wiener process, and dq is the Poisson process. The random variable repre...

Following the economic rationale of [7] and [8] we present a new class of Asian options where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in this is a protection feature which is key to t...