A framework for pricing Asian power options is developed when the underlying asset follows a jumpfraction process. The partial differential equation (PDE) in the fractional environment with jump is constructed for such option using general Itô's lemma and self-financing dynamic strategy. With...

Maximum-minimum bidirectional options are a kind of exotic path dependent options. In the constant elasticity of variance (CEV) model, a combining trinomial tree was structured to approximate the non-constant volatility that is a function of the underlying asset. On this basis, a simple and...

A framework for pricing Asian power options is developed when the underlying asset follows a jumpfraction process. The partial differential equation (PDE) in the fractional environment with jump is constructed for such option using general Itô's lemma and self-financing dynamic strategy. With...

We will present a model to compute a lower bound for the price of this option. The model, represented by a non-linear parabolic PDE, is implemented with finite elements in order to demonstrate the results with several derivatives from the European market.

Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of...

In Kusuda [45], we developed equilibrium analysis in security market economy with jump-Wiener information where no finite number of securities can complete markets. Assuming approximately complete markets (Björk et al. [11] [12]) in which a continuum of bonds are traded and any contingent claim...

This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. It consists in determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining...

Risk neutral densities (RND) can be used to forecast the price of the underlying basis for the option, or it may be used to price other derivates based on the same sequence. The method adopted in this paper to calculate the RND is to firts estimate daily the diffusion process of the underlying...

We estimate the process underlying the pricing of American options by using higher-order lattices combined with a multigrid method. This paper also tests whether the risk-neutral densities given from American options provide a good forecasting tool. We use a nonparametric test of the densities...

We explain the valuation and correlation hedging of Foreign Exchange Basket Options in a multi-dimensional Black-Scholes model that allows including the smile. The technique presented is a fast analytic approximation to an accurate solution of the valuation problem.