For its theoretical interest and strong impact on financial markets, option valuation is considered one of the cornerstones of contemporary mathematical finance. This paper specifically studies the valuation of exotic options with digital payoff and flexible payment plan. By means of the Incomplete Fourier Transform, the pricing problem is solved in order to find integral representations of the...

An installment option is a European option in which the premium, instead of being paid up-front, is paid in a series of installments. If all installments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option lapses with no further payments on either side. We discuss pricing and risk management for these ...

The pricing problem for a continuous path-dependent option results in a path integral which can be recast into an infinite-dimensional integration problem. We study ANOVA decomposition of a function of infinitely many variables arising from the Brownian bridge formulation of the continuous option pricing problem. We show that all resulting ANOVA terms can be smooth in this infinite-dimensional ...

In this paper, we consider the pricing problem for extremum options by constructing a double nonaffine stochastic volatility model. The joint characteristic function of logarithm two asset prices is derived using Feynman–Kac theorem and one-order Taylor approximation expansion. semiclosed analytical formulas European including option on maximum minimum underlying assets are measure change techn...

Liu process is a new tool to deal with the noise process based on uncertainty theory. In this paper, we view the foreign exchange rate as an uncertain process, described by an uncertain differential equation driven by Liu process, and build an uncertain currency model. Then the uncertain currency option processes are discussed. Moreover, European and American currency option pricing formulas ar...

The aim of the paper is to develop pricing formulas for European type Asian options written on the exchange rate in a two currency economy. The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions. As a special case of a discrete Asian option we analyse the delayed payment currency option and develop closed form pricing and h...

Closed sets of finitely-additive probabilities are statistical laws of statistically unstable random phenomena. Decision theory, adapted to such random phenomena, is applied to the problem of valuation of European options. Embedding of the Arrow-Debreu state preference approach to options pricing into decision theoretical framework is achieved by means of considering option prices as decision v...

In this paper, a new radial basis function (RBF) approach is developed for solving European option pricing model. Without any simplifications, a simple discretization pattern directly leads to a system Ax = b, moreover, employing a new variable shape parameter (VSP) strategy named binary shape parameter (BSP) strategy leads to more accurat results rather than constant shape parameter (CSP) stra...

Alternatives to the Black-Scholes-Vasicek deflator introduced in [25] are proposed. They are based on the multivariate Wang variance-gamma process considered in [66]. As an application, closed form analytical multiple integral formulas for pricing the European geometric basket option with a deflated multivariate exponential Wang variance-gamma asset pricing model are derived. Mathematics Subjec...

In this paper, we consider two types of pricing option in financial markets using quasi Monte Carlo algorithm with variance reduction procedures. We evaluate Asian-style and European-style options pricing based on Black-Scholes model. Finally, some numerical results presented.