A Parabolic Variational Inequality Arising from the Valuation of Strike Reset Options∗
نویسندگان
چکیده
A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C∞ smoothness of the free boundary are proven in some situations.
منابع مشابه
Valuation of European Installment Put Options — Variational Inequality Approach 1
Abstract: In this paper we consider a parabolic variational inequality arising from the valuation of European installment put options. We prove the existence and uniqueness of the solution to the problem. Moreover, we obtain C∞ regularity and the bounds of the free boundary. Eventually we show its numerical result by the binomial method.
متن کاملFinite Volume Methods for the Valuation of American Options
Abstract. We consider the use of finite volume methods for the approximation of a parabolic variational inequality arising in financial mathematics. We show, under some regularity conditions, the convergence of the upwind implicit finite volume scheme to a weak solution of the variational inequality in a bounded domain. Some results, obtained in comparison with other methods on two dimensional ...
متن کاملNumerical Treatment of the Black-Scholes Variational Inequality in Computational Finance
Among the central concerns in mathematical finance is the evaluation of American options. An American option gives the holder the right but not the obligation to buy or sell a certain financial asset within a certain time-frame, for a certain strike price. The valuation of American options is formulated as an optimal stopping problem. If the stock price is modelled by a geometric Brownian motio...
متن کاملThe Regularization Method for a Degenerate Parabolic Variational Inequality Arising from American Option Valuation
Option trading forms part of our financial markets. A traded option gives to its owner the right to buy (call option) or to sell (put option) a fixed quantity of assets of a specified stock at a fixed price (exercise or strike price). There are two major types of traded options. One is the American option that can be exercised at any time prior to its expiry date, and the other option, which ca...
متن کاملOn the Valuation of Options in Jump-Diffusion Models by Variational Methods∗
We consider the valuation of European and American-style options under jump-diffusion processes by variational methods. In particular, the value function is seen to satisfy a parabolic partial (spatial) integro-differential variational inequality. A theoretical framework is developed and an analysis of a Þnite element implementation presented. A key feature is the introduction of separate appro...
متن کامل