Option pricing is the the core content of modern finance. American option is widely accepted by investors for its flexibility of exercising time. In this paper, American option pricing formula is calculated for uncertain financial market and some mathematical properties of them are discussed. In addition, some examples are proposed. keywords: finance, uncertain process, option pricing

The central part of pricing agricultural commodity futures options is to find appropriate stochastic process of the underlying assets. The Black’s (1976) futures option pricing model laid the foundation for a new era of futures option valuation theory. The geometric Brownian motion assumption girding the Black’s model, however, has been regarded as unrealistic in numerous empirical studies. Opt...

Options pricing model parameters are inherently imprecise due to fluctuations in the real-world financial market. Traditional option pricing methods do not account for the uncertainty in parameters, but the fuzzy set theory may be applicable. This paper proposes a cash-or-nothing European call binary option pricing model based on the hypothesis that the underlying asset price, risk-free rate of...

In this work we study the multilayer adsorption of polyatomic species on homogeneous and heterogeneous bivariate surfaces. A new approximate analytic isotherm is obtained and validated by comparing with Monte Carlo simulation. Then, we use the well-known Brunauer-Emmet-Teller’s (BET) approach to analyze these isotherms and to estimate the monolayer volume, vm. The results show that the value of...

This paper describes and analyses the history of the fundamental equation of modern financial economics: the Black-Scholes (or Black-Scholes-Merton) option pricing equation. In that history, several themes of potentially general importance are revealed. First, the key mathematical work was not rule-following but bricolage, creative tinkering. Second, it was, however, bricolage guided by the goa...

This paper presents a method for evaluating the reliability of an in-service highway bridge that considers the resistance capacity loss due to various corrosive environments. To demonstrate the application of the suggested method, a pre-stressed concrete-I (PSC-I) type girder was selected as a sample bridge. An analytical procedure was developed to quantitatively evaluate the performance degrad...

In this paper, installment options on the underlying asset which evolves according to Black-Scholes model and pays constant dividend to its owner will be considered. Applying arbitrage pricing theory, the non-homogeneous parabolic partial differential equation governing the value of installment option is derived. Then, penalty method is used to value the European continuous installment call opt...

This paper aims to provide a practical example on the assessment and propagation of input uncertainty for option pricing when using tree-based methods. Input uncertainty is propagated into output uncertainty, reflecting that option prices are as unknown as the inputs they are based on. Option pricing formulas are tools whose validity is conditional not only on how close the model represents rea...