The Pricing of A Moving Barrier Option

We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relation with risk free rate, dividend rate and stock volatility.Comment: 11 pages, written in working paper series in 200

The Pricing of Multiple-Expiry Exotics

In this paper we extend Buchen's method to develop a new technique for pricing of some exotic options with several expiry dates(more than 3 expiry dates) using a concept of higher order binary option. At first we introduce the concept of higher order binary option and then provide the pricing formulae of $n$-th order binaries using PDE method. After that, we apply them to pricing of some multiple-expiry exotic options such as Bermudan option, multi time extendable option, multi shout option and etc. Here, when calculating the price of concrete multiple-expiry exotic options, we do not try to get the formal solution to corresponding initial-boundary problem of the Black-Scholes equation, but explain how to express the expiry payoffs of the exotic options as a combination of the payoffs of some class of higher order binary options. Once the expiry payoffs are expressed as a linear combination of the payoffs of some class of higher order binary options, in order to avoid arbitrage, the exotic option prices are obtained by static replication with respect to this family of higher order binaries.Comment: 16 pages, 3 figures, Ver. 1 was presented in the 1st International Conference of Pyongyang University of Science & Technology, 5~6, Oct, 2011, in ver. 2 added proof, in ver. 3 revised and added some detail of proofs, Ver. 4,5: latex version, Ver. 6~8: corrected typos in EJMAA Vol.1(2)2013,247-25

A construction of fractal surfaces with function scaling factors on a rectangular grid

A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces constructed. We construct IFS with function vertical scaling factors which are 0 on the boundaries of a rectangular grid using arbitrary data set on a rectangular grid and give a condition for an attractor of the IFS constructed being a surface. Finally, lower and upper bounds of Box-counting dimension of the constructed surface are estimated.Comment: 9 pages, 2 figure

Construction of Fractal Surfaces by Recurrent Fractal Interpolation Curves

A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible constructions of fractal surfaces.Comment: 14 pages, 2 figure

Analytical Pricing of Defaultable Bond with Stochastic Default Intensity

We provide analytical pricing formula of corporate defaultable bond with both expected and unexpected default in the case with stochastic default intensity. In the case with constant short rate and exogenous default recovery using PDE method, we gave some pricing formula of the defaultable bond under the conditions that 1)expected default recovery is the same with unexpected default recovery; 2) default intensity follows one of 3 special cases of Willmott model; 3) default intensity is uncorrelated with firm value. Then we derived a pricing formula of a credit default swap. And in the case of stochastic short rate and exogenous default recovery using PDE method, we gave some pricing formula of the defaultable bond under the conditions that 1) expected default recovery is the same with unexpected default recovery; 2) the short rate follows Vasicek model; 3) default intensity follows one of 3 special cases of Willmott model; 4) default intensity is uncorrelated with firm value; 5) default intensity is uncorrelated with short rate. Then we derived a pricing formula of a credit default swap. We give some credit spread analysis, too.Comment: 35 pages, 6 figures; written in working paper series in 2005, version 3 added references with crossref and revised introductio

Equiaffine Structure and Conjugate Ricci-symmetry of a Statistical Manifold

A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [2] and [3]. In this paper, a fact that a statistical manifold, which is conjugate Ricci-symmetric, has an equiaffine structure is given, where conjugate Ricci-symmetry is weaker condition than conjugate symmetry. A condition for conjugate symmetry and conjugate Ricci-symmetry to coincide is also given.Comment: 7 page

Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and nn terms

This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.Comment: 15 pages, ver 5 corrected 4 typos in ver 4; this version to appear in FCAA Vol.17, No.1, 2014 with the title "Operation Method for Solving Multi-Term Fractional Differential Equations with the Generalized Fractional Derivatives

Numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon

Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's structural model [1] for discrete coupon bonds into a unified 2 factor model of structural and reduced form types and we study a numerical analysis for it by explicit finite difference scheme. These equations are parabolic equations with 3 variables and they include mixed derivatives, so the explicit finite difference scheme is not stable in general. We find conditions for the explicit finite difference scheme to be stable, in the case that it is stable, numerically compute the price of the bond and analyze its credit spread and duration.Comment: 15 pages, 12 figure

Pricing Corporate Defaultable Bond using Declared Firm Value

We study the pricing problem for corporate defaultable bond from the viewpoint of the investors outside the firm that could not exactly know about the information of the firm. We consider the problem for pricing of corporate defaultable bond in the case when the firm value is only declared in some fixed discrete time and unexpected default intensity is determined by the declared firm value. Here we provide a partial differential equation model for such a defaultable bond and give its pricing formula. Our pricing model is derived to solving problems of partial differential equations with random constants (de- fault intensity) and terminal values of binary types. Our main method is to use the solving method of a partial differential equation with a random constant in every subinterval and to take expectation to remove the random constants.Comment: 12 pages, version 5 is written in tex and accepted in EJMAA(Electronic Journal of Mathematical Analysis and Applications

Variational inequality for perpetual American option price and convergence to the solution of the difference equation

A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual American option are proved. Then the maximum principle, the existence and uniqueness of the solution to the difference equation corresponding to the variational inequality for pricing the perpetual American option and the solution representation are provided and the fact that the solution to the difference equation converges to the viscosity solution to the variational inequality is proved. It is shown that the limits of the prices of variational inequality and BTM models for American Option when the maturity goes to infinity do not depend on time and they become the prices of the perpetual American option.Comment: 23 page