Doobae Jun

PRICING CHAINED OPTIONS WITH CURVED BARRIERS

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 when two or more barrier options with exponential barriers are chained together. We then extend the results to the options with general curved barriers.

THE UNIFORM CLT FOR MARTINGALE DIFFERENCE ARRAYS UNDER THE UNIFORMLY INTEGRABLE ENTROPY

In this paper we consider the uniform central limit theorem for a martingale-diere nce array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-diere nce arrays of process indexed by a class of measurable functions by a method as Ziegler (19) did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-diere nce and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler (19) and other results of independent problems. The results also generalizes those of Bae and Choi (3) to martingale-diere nce array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.

Continuity correction for discrete barrier options with two barriers

Discrete barrier options are the options whose payoffs are determined by underlying prices at a finite set of times. We consider the discrete barrier option with two barriers. Broadie et al. (1997) [16] proposed a continuity correction for the discretely monitored barrier option. We extend this idea to barrier option with two barriers. The proof for discrete chained barrier option is provided and numerical results show the continuity correction approximation is remarkably accurate.

A New Approach of Box‐Müller Method

This paper gives a new approach of the Box‐Muller Method which transfer a standard uniform distribution to a standard normal distribution. We divide two dimensional unit space (0,1)2 into 15 parts (i.e. hold, rise, slowly rise, sharp rise, fall, slowly fall, sharp fall parts) which show the direction of future commodity prices. Then we can predict the price of commodity in future and manage the risk of uncertain value to come.