The aim of this paper is to provide a semimartingale approximation of a fractional stochastic integration. This result leads us to approximate the fractional Black-Scholes model by a model driven by semimartingales, and a European option pricing formula is found. 2000 AMS Classification: 60H05, 65G15, 62P05.

We discuss option pricing problems under a new model of stock fluctuations. This model captures the information distribution among investors by adjoining a hidden Markov process to the Black-Scholes exponential Brownian motion model. We provide new valuations for various standard hedge options, such as European, perpetual American and look-back options.

In this paper, we take the advantage of high frequency data to develop option pricing model and select the Realized GARCH model to describe the volatility of assets, use NIG distribution to describe the distribution of underlying assets, and also build the Realized-GARCH-NIG model to price the option. Finally, we obtain the dynamic option pricing model based on the Realized-GARCH-NIG approach. ...

In this paper we analyze a nonlinear generalization of the Black-Scholes equation for pricing American style call option in which the volatility may depend on the underlying asset price and the Gamma of the option. We propose a novel method of pricing American style call options by means of transformation of the free boundary problem for a nonlinear Black-Scholes equation into the so-called Gam...

In this paper, we investigate two numerical methods for pricing Asian options: Laplace transform inversion and Monte Carlo simulation. In attempting to numerically invert the Laplace transform of the Asian call option that has been derived previously in the literature, we point out some of the potential difficulties inherent in this approach. We investigate the effectiveness of two easy-to-impl...

An installment option is a European option in which the premium, instead of being paid up-front, is paid in a series of installments. If all installments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option lapses with no further payments on either side. We discuss pricing and risk management for these ...

Abstract This article addresses the problem of pricing European options when underlying asset is not perfectly liquid. A liquidity discounting factor as a function market-wide governed by mean-reverting stochastic process and sensitivity price to firstly introduced, so that impact on can be captured option model. The characteristic analytically worked out using Feynman–Kac theorem closed-form f...

Motivated by applications in Asian option pricing, optimal commodity trading etc., we propose a splitting scheme for fully nonlinear degenerate parabolic PDEs. The splitting scheme generalizes the probabilistic scheme of Fahim, Touzi and Warin [13] to the degenerate case. General convergence as well as rate of convergence are obtained under reasonable conditions. In particular, it can be used f...

A lookback option is an exotic that allows investors to look back at the underlying prices occurring over life of option, and exercise right assets optimal point. This paper proposes a mean-reverting stock model investigate in uncertain environment. The call put options pricing formulas are derived, corresponding numerical algorithms designed compute these two optio...