A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation ...

In this paper we propose a general foreign equity option pricing framework that unifies the vast foreign equity option pricing literature and incorporates the stochastic volatility into foreign equity option pricing. Under our framework, the time-changed Lévy processes are used to model the underlying assets price of foreign equity option and the closed form pricing formula is obtained through ...

Modern option pricing techniques are often considered among the most mathematically complex of all applied areas of financial engineering. In particular these techniques derive their impetus from four milestones of option pricing models: Bachelier model, Samuelson model, Black-Scholes-Merton model and Levy model. In this paper we evaluate all related option pricing models based on these milesto...

In the following paper, we provide a review and development of sequential Monte Carlo (SMC) methods ([17, 18, 24]) for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used, successfully, for a wide class of applications in engineering, statistics and physic...

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...

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...

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...