This paper studies the probability distribution and option pricing for drawdown in a stochastic volatility environment. Their analytical approximation formulas are derived by the application of a singular perturbation method (Fouque et al., 2000). The mathematical validity of the approximation...

Asymptotic expansions are made for the distributions of the Maximum Empirical Likelihood (MEL) estimator and the Estimating Equation (EE) estimator (or the Generalized Method of Moments (GMM) in econometrics) for the coefficients of a single structural equation in a system of linear simultaneous...

This paper reviews the asymptotic expansion approach based on Malliavin-Watanabe Calculus in Mathematical Finance. We give the basic formulation of the asymptotic expansion approach and discuss its power and usefulness to solve important problems arised in nance. As illustrations we use three...

We shall generalize the Black-Scholes option pricing formula by incorporating stochastic interest rates. Although the existing literatures have obtained some formulae for stock options under stochastic interest rates, the closed-form solutions have been known only under the Gaussian (Merton...

We propose the conditional limited information maximum likelihood (CLIML) approach for estimating dynamic panel structural equation models. When there are dynamic effects and endogenous variables with individual effects at the same time, the CLIML estimation method for the doubly-filtered data...