Takahiko Fujita

A Note on the Joint Distribution of α, β-Percentiles and Its Application to the Option Pricing

In this paper, using Laplace transform, we will calculate the joint density of twopercentiles of stock prices in the Black–Sholes model and make the price of exchange options of such twopercentiles.

Pricing Derivatives in Zone Model

In this paper, we propose a new interest rate model with a zone as ageneralization of C.I.R. model. Using a perturbation method, we can have anapproximation price of interest derivatives in our model.

The distribution of continuous time rank processes

In this paper, we will give exact calculations of probability disrtributions of continuous rank processes in Brownian case, Brownian motion with drift case, Pinned Brownian motion case. These calculations are based on the results of the joint distributions of Brownian motion and its soujourn time. Also we give new exotic options using rank statistics and calculate the price of rank options.