Abstract. External barrier options are two-asset options with stochastic variables where the payoff depends on one underlying asset and the barrier depends on another state variable. The barrier state variable determines whether the option is knocked in or out when the value of the variable is above or below some prescribed barrier level. This paper derives the explicit analytic solution of the...

In this paper we provide a smoothed perturbation analysis (SPA) of the sensitivity of a discrete time Parisian option with respect to the barrier level. The analysis put forward is of interest in a broader context than that of exotic options as we provide an SPA analysis for a problem where the critical event for the SPA estimator is based on an entire sample path, which is a novelty in the lit...

A new kind of option called hereafter a Parisian barrier option is studied in this paper This option is the following variant of the so called barrier option a down and out barrier option becomes worthless as soon as a barrier is reached whereas a down and out Parisian barrier option is lost by the owner if the underlying asset reaches a prespeci ed level and remains constantly below this level...

A barrier option is an option whose payoff depends on whether the price path of the underlying asset ever reaches certain predetermined price levels called the barriers. A single(double-) barrier option is a barrier option with one (two, respectively) barrier(s). No simple and exact closed-form pricing formula for double-barrier options has been reported in the literature. This paper proposes a...

The extension of the Black{Scholes option pricing theory to the valuation of barrier options is reconsidered. Working in the binomial framework of CRR we show how various types of barrier options can be priced either by backward induction or by closed binomial formulas. We also consider analytically and numerically the convergence of the prices in discrete time to their continuous{time limits. ...

A barrier option is an otherwise vanilla call or put option with a strike of X but with an extra parameter B, the barrier: the option only comes into existence (is knocked in) or is terminated (is knocked out) if the spot price crosses the barrier during the life of the option. Because there is a positive probability (in either case) of worthlessness, these options are cheaper than the correspo...

As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others i...

This paper studies barrier options which are chained together, each with payoff contingent on curved barriers. When the underlying asset price hits a primary curved barrier, a secondary barrier option is given to a primary barrier option holder. Then if the asset price hits another curved barrier, a third barrier option is given, and so on. We provide explicit price formulas for these options w...

Exotic option contracts typically specify a contingency upon an underlying asset price monitored at a discrete set of times. Yet, techniques used to price such options routinely assume continuous monitoring leading to often substantial price discrepancies. A brief review of relevant option-pricing methods is presented. The pricing problem is transformed into one of Wiener–Hopf type using a z-tr...