Nonexpansive Maps and Option Pricing
نویسنده
چکیده
The famous Black-Sholes (BS) and Cox-Ross-Rubinstein (CRR) formulas are basic results in the modern theory of option pricing in financial mathematics. They are usually deduced by means of stochastic analysis; various generalisations of these formulas were proposed using more sophisticated stochastic models for common stocks pricing evolution. In this paper we develop systematically a deterministic approach to the option pricing that leads to a different type of generalisations of BS and CRR formulas characterised by more rough assumptions on common stocks evolution (which are therefore easier to verify). On the other hand, this approach is more elementary, because it uses neither martingales nor stochastic equations.
منابع مشابه
Game theoretic analysis of incomplete markets: emergence of probabilities, nonlinear and fractional Black-Scholes equations
Expanding the ideas of the author’s paper ’Nonexpansive maps and option pricing theory’ (Kibernetica, 34:6, 1998, 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral probabilities emerge automatically from the robust control evaluation. This approach seems to be especially appealing for incomplete markets encompassing extensive, so ...
متن کاملHow Does Pricing of Day-ahead Electricity Market Affect Put Option Pricing?
In this paper, impacts of day-ahead market pricing on behavior of producers and consumers in option and day-ahead markets and on option pricing are studied. To this end, two comprehensive equilibrium models for joint put option and day-ahead markets under pay-as-bid and uniform pricing in day-ahead market are presented, respectively. Interaction between put option and day-ahead markets, uncerta...
متن کاملNumerical Solutions for Fractional Black-Scholes Option Pricing Equation
In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.
متن کاملOption Pricing on Commodity Prices Using Jump Diffusion Models
In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian commodity prices fluctuations. We used the daily closed Unwashed Lekempti grade 5 (ULK5) coffee and Whitish Wollega Sesame Seed Grade3 (WWSS3) prices obtained from Ethiopia commodity exchange (ECX) market to analyse the prices fluctuations.The natures of log-returns of the prices exhibit a...
متن کاملA New Stock Model for Option Pricing in Uncertain Environment
The option-pricing problem is always an important part in modern finance. Assuming that the stock diffusion is a constant, some literature has introduced many stock models and given corresponding option pricing formulas within the framework of the uncertainty theory. In this paper, we propose a new stock model with uncertain stock diffusion for uncertain markets. Some option pricing formulas on...
متن کامل