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This paper proposes a new local linearization method which approximates a nonlinear stochastic differential equation by a linear stochastic differential equation. Using this method, we can estimate parameters of the nonlinear stochastic differential equation from discrete observations by the maximum likelihood technique. We conduct the numerical experiments(More)
This paper investigates the rate of convergence of an alternative approximation method for stochastic differential equations. The rates of convergence of the one-step and multi-step approximation errors are proved to be O((∆t)2) and O(∆t) in the Lp sense respectively, where ∆t is discrete time interval. The rate of convergence of the one-step approximation(More)
The existing literature on credit risk valuation does not have a consensus on whether credit risk can explain the observed corporate-Treasury yield spreads. The purpose of this article is to estimate the investors’ risk aversion of corporate bond market and to explain the credit spreads. We show that how much of the credit spreads is due to credit risk, and(More)
This paper provides a semiparametric model to estimate processes of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we estimate the volatility process by filtering. We prove the consistency of the model in the sense that estimated processes(More)
  • Isao Shoji
  • Statistical Methods and Applications
  • 2013
This paper discusses nonparametric estimation of nonlinear dynamical system models by a method of metric-based local linear approximation. We assume no functional form of a givenmodel but estimate it from experimental data by approximating the curve implied by the function by the tangent plane around the neighborhood of a tangent point. To specify an(More)
We propose an analytical approximation of the term structure of interest rates under general diffusion processes of the short-rate and state variables. A method of approximating conditional moments as the solution to a system of ordinary differential equations is applied to the pricing of bonds. Numerical experiments based on two illustrative models show(More)
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