This paper mainly discusses the American option’s hedging strategies via binomial model and the basic idea of pricing and hedging American option. Although the essential scheme of hedging is almost the same as European option, small differences may arise when simulating the process for American option holder has more rights, spelling that the option can be exercised at anytime before its maturi...

Numerical methods are developed for pricing European and American options under Kou’s jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a...

We describe the automatic generation of nite diierence codes for solving the Black-Scholes and related equations for option valuation using the SciNapse software synthesis system. Analysts can specify codes at a very high level that mirrors the mathematical description of the problem. A typical option pricing speciication occupies less than a half page. From such concise input, the system autom...

Han, Chuan-Hsiang. Singular Perturbations on Non-Smooth Boundary Problems in Finance. (Under the direction of Jean-Pierre Fouque.) In this work we apply asymptotic analysis on compound options, American options, Asian options, and variance (or volatility) contracts in the context of stochastic volatility models. Singular perturbation techniques are primarily used. A singular-regular perturbatio...

An alternative option pricing model is proposed, in which the asset prices follow the jump-diffusion and exhibits mean reversion. The stochastic volatility follows the jump-diffusion with mean reversion. We find a formulation for the European-style option in terms of characteristic functions.

Jaume Masoliver‡ Departament de F́ısica Fonamental, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Spain (Dated: May 28, 2008) Abstract We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a ...

In this work, we apply He’s variotional iteration method for obtaining analytic solutions to nonlinear Black-Scholes equation with boundary conditions for European option pricing problem. The analytical solution of the equation is calculated in the form a convergent power series with easily computable components. The powerful VIM method is capable of handling both linear and non-linear equation...

In this paper, we investigate option valuation problems under the fractional Black–Scholes model. The aim is to propose a pricing formula for the European option with transaction costs, where the costs structure contains fixed costs, a cost propositional to the volume traded, and a cost proportional to the value traded. Precisely, we provide an approximate solution of the nonlinear Hoggard–Whal...