Youngsoo Choi

A Note on Series Approximation of Transition Density of Diffusion Processes

Modelling financial phenomena with diffusion processes is frequently used technique. This study reviews the earlier researches on the approximation problem of transition densities of diffusion processes, which takes important roles in estimating diffusion processes, and consider the method to obtain the coefficients of series efficiently, in series approximation method of transition densities. We developed a new efficient algorithm to compute the coefficients which are represented by repeated Dynkin operator on Hermite polynomial.

Information Content in Sneer Asymmetry: An Application to OOS Implied Volatility Forecasting

The ad hoc Black-Scholes (AHBS) is one of the most widely used option valuation models among practitioners. The main contribution of this study is that we improve the out-of-sample forecast accuracy of the AHBS model. First, we make the empirical observation that the call and put sneers are discontinuous and have different slopes when moneyness is equal to one. Next, we propose a new data usage methodology that incorporates the information contained in the asymmetric response of the call and put sneers. Our new method provides more accurate out-of-sample forecasts for several intraday time horizons. Our results are robust across several dimensions, including time period, forecast horizon, moneyness, and model specification.

A Simple Model of the Nominal Term Structure of Interest Rates

This paper presents a simple two-factor model of nominal term structure of interest rates, in which the log-price kernel has an autoregressive drift process and a nonlinear GARCH volatility process. With these two state-variable processes, closed-form solutions are derived for zero-coupon bond prices as well as yield to maturity for a given time to maturity.

A Brief Review of a Term Saddlepoint Approximation Method for Estimating Diffusion Processes

Recently various methods were suggested and reviewed for estimating diffusion processes. Out of suggested estimation method, we mainly concerns on the estimation method using saddlepoint approximation method, and we suggest a term saddlepoint approximation(ASP) method which is the simplest saddlepoint approximation method. We will show that ASP method provides fast estimator as much as Euler approximation method(EAM) in computing, and the estimator also has good statistical properties comparable to the maximum likelihood estimator(MLE). By simulation study we compare the properties of ASP estimator with MLE and EAM, for Ornstein-Uhlenbeck diffusion processes.

Mathematical Review on the Local Linearizing Method of Drift Coefficient

Modeling financial phenomena with diffusion processes is a commonly used methodology in the area of modern finance. Recently, various types of diffusion models have been suggested to explain the specific financial processes, and their related inference methodology have been also developed. In particular, likelihood methods for the efficient and accurate inference have been explored in various ways. In this paper, we review the mathematical properties of an approximated likelihood method, which is obtained by linearizing the drift coefficient of a diffusion process.

Option Pricing and Sensitivity Evaluation Methodology: Improvement of Speed and Accuracy

This paper presents how to improve the efficiency and accuracy in the pricing and sensitivity evaluation for derivatives, since the need for the evaluation of complicated derivatives is increased. The Monte Carlo(MC) simulation using the quasi random number instead of pseudo random number can improve the elapsed time and accuracy for the valuation of European-type derivatives. However, the quasi MC simulation method has its limit for applying it in the multi-dimensional case such as American-type and path-dependent options due to the increased correlation between dimensions as the dimension of random numbers is increased. In order to complement this problem, we develop a modified method in which correlation values are controlled to be below a pre-specified value. Thus, this method is applicable for the pricing of either derivatives ill which underlying assets or risk factors are several or derivatives having path-dependent or early redemption property. Furthermore, we illustrate that it is important to take an appropriate grid interval for the use of finite difference method(FDM) by applying the FDM to one example of non-symmetrical butterfly spreads.