arXiv subjects

Jirô Akahori

Publications and source records attributed to Jirô Akahori.

25 records · Page 2Linked to original sources

arXiv2009

Calibration of transparency risks: a note

The aim of this research is to give a simple framework to evaluate/quantize the "transparency" of a firm. We assume that the process of the firm value is only observable once in a while but is strongly correlated with the stock price which is observable and tradable. This hybrid type structure make the transparency "observable". The implication of the present study is that the depth of the shock to the market caused by the precise accounting information does reflect the degree of transparency. Furthermore, it can be quantized resorting to the calibration method.

q-fin.RM↗

arXiv2006

What is the natural scale for a Lévy process in modelling term structure of interest rates?

This paper gives examples of explicit arbitrage-free term structure models with Lévy jumps via state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a Lévy process is a "natural" scale for the process to be the state variable of a market.

math.PR↗

arXiv2006

A Discrete Itô Calculus Approach to He's Framework for Multi-Factor Discrete Markets

In the present paper, a discrete version of Itô's formula for a class of multi-dimensional random walk is introduced and applied to the study of a discrete-time complete market model which we call He's framework. The formula unifies continuous-time and discrete-time settings and by regarding the latter as the finite difference scheme of the former, the order of convergence is obtained. The result shows that He's framework cannot be of order 1 scheme except for the one dimensional case.

math.PR↗

arXiv2006

Generalizations of Ho-Lee's binomial interest rate model I: from one- to multi-factor

In this paper a multi-factor generalization of Ho-Lee model is proposed. In sharp contrast to the classical Ho-Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is stationary to be compatible with principal component analysis. Based on the model, generalizations of duration-based hedging are proposed. A continuous-time limit of the model is also discussed.

math.PR↗

arXiv2006

Local Time in Parisian Walkways

In the present paper, Ito formula and Tanaka formula for a special kind of symmetric random walk in the complex plain are studied. The random walk is called Parisian walk, and its local time is defined to be the number of exit from some regions.

math.PR↗

arXiv2006

Discrete Itô Formulas and Their Applications to Stochastic Numerics

This is a survey note of the author's observations on the discrete-time analogues of Itô formulas.

math.PR↗

arXiv2006

Stochastic equation on compact groups in discrete negative time

In this paper a stochastic equation on compact groups in discrete negative time is studied. This is closely related to Tsirelson's stochastic differential equation, of which any solution is non-strong. How the group action reflects on the set of solutions is investigated. It is applied to generalize Yor's result and give a necessary and sufficient condition for existence of a strong solution and for uniqueness in law.

math.PR↗