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 develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a closed-form approximate solution, which relies on the expansion of the intractable model around an “auxiliary” one. We...

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...

A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram-Charlier series expansion, known as the Gauss-Hermite expansion. This expansion converges for...

The Finite Element Method is a well-studied and well-understood method of solving partial differential equations. It's applicability to financial models formulated as PDEs is demonstrated. It's advantage concerning the computation of accurate "Greeks" is delineated. This is demonstrated with...

When using an Euler discretisation to simulate a mean-reverting square root process, one runs into the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this...

At the time of writing this article, Fourier inversion is the computational method of choice for a fast and accurate calculation of plain vanilla option prices in models with an analytically available characteristic function. Shifting the contour of integration along the complex plane allows for...