This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in an asymptotic expansion approach. First, the paper derives an asymptotic expansion for generalized Wiener functionals. After it is appl...

This paper explores the utility of a discrete singular convolution (DSC) algorithm for solving the Black–Scholes equation. Both European and American style options, which include all nontrivial plain option pricing problems, are considered to test the accuracy and to examine the efficiency of the present algorithm. Adaptive meshes are constructed to enhance the performance of the DSC algorithm....

This paper introduces the notion of option pricing in the context of financial markets. The discrete time, one-period binomial model is explored and generalized to the multi-period binomial model. The multi-period model is then redeveloped using the sophisticated tools of martingale theory. The paper concludes with a brief extension of the results to continuous time, giving a heuristic derivati...

this paper studies housing choice under fuzzy circumstances. in this article, fuzzy distance method is employed for selection process. methodology of housing choice with fuzzy distance approach is based on the minimizing fuzzy distance of features from desired amount under fuzzy condition. meanwhile, in the discrete choice models, housing choice is based on utility maximizing of available optio...

Barrier options were first priced by Merton in 1973 using partial differential equation. In this work, we present a closed form formula for pricing European barrier option with a moving barrier that increases with time to expiration. We adopted a three-step approach which include; justifying that barrier options satisfy the Black-Scholes partial differential equation under certain conditions, p...

We consider the problem of semistatic hedging of a single barrier option in a model where the underlying is a time-homogeneous diffusion, possibly running on an independent stochastic clock. The main result of the paper is an analytic expression for the payoff of a European-type contingent claim, which has the same price as the barrier option up to hitting the barrier. We then consider some exa...

Based upon the Fourier series expansion, we propose a simple and easy-to-use approach for computing accurate estimates of Black-Scholes double barrier option prices with time-dependent parameters. This new approach is also able to provide tight upper and lower bounds of the exact barrier option prices. Furthermore, this approach can be straightforwardly extended to the valuation of standard Eur...

In this paper two different methods are presented to approximate the solution of the fractional Black-Scholes equation for valuation of barrier option. Also, the two schemes need less computational work in comparison with the traditional methods. In this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...

We introduce MEMORAX, a tool for the verification of control state reachability (i.e., safety properties) of concurrent programs manipulating finite range and integer variables and running on top of weak memory models. The verification task is non-trivial as it involves exploring state spaces of arbitrary or even infinite sizes. Even for programs that only manipulate finite range variables, the...