Warrant Pricing Models And Its Empirical Research

As a financial derivative product, warrants have hedging, risk aversion, arbitrage, speculation, value discovery and many other functions. And over the past decades, warrants have become an important component of financial derivatives market. As a consequence, how to price them reasonably and how to estimate the parameters of the warrant pricing models efficiently have become a difficulty and a hot spot of warrant pricing study for scholars, investors and financial institutions. Since the1970s, the Black-Scholes (B-S) model is the most widely used model to calculate warrant prices. However, a lot of empirical evidence suggests that asset return distributions are not normally distributed but instead have been shown to exhibit patterns of leptokurtosis, heavy tails and skewness, and also volatility of asset return is not a constant but in fact varies significantly through time and often exhibits the volatility clustering. These stylized facts indicate that the assumption of underlying asset return follows a normal distribution with constant volatility in the B-S model is incorrect. As a result, the warrant prices calculated by using the B-S model deviate from the actual market prices, and the well-known "volatility smile" cannot be captured in the B-S model. Therefore, the classical B-S model need to be extended. Hence, developing alternative warrant pricing models and estimating the unknown parameters of these warrant pricing models is of great theoretical value and practical significance for determining the reasonable values of the warrants.Based on the combination of theoretical and empirical insights, this dissertation presents a thorough study of warrant pricing and parameter estimation. The main contributions of this dissertation are as follows:First, this dissertation develops method for maximum likelihood estimation of the parameters of warrant pricing models. Monte Carlo simulations are presented to examine the accuracy and small sample properties of the maximum likelihood estimators. Numerical results demonstrate that, based on accurate closed-form approximations to the transition function of diffusion model, the means of maximum likelihood estimators of the parameters related to warrant pricing are very closed to the ture values. Thus, the maximum likelihood method based on transity density approximation is very efficient for estimating diffusion model. In order to estimate the parameters of the stochastic volatility model, this dissertation presents a maximum likelihood method based on efficient importance sampling (EIS) procedure. Numerical results demonstrate that the EIS-based maximum likelihood (EIS-ML) method performs very well. Even in the case of small sample size, the means of the EIS-ML estimators are very close to the true values. Hence the EIS-ML method is very efficient. In addition, numerical results also show that the EIS-ML method has very good convergence and high computational efficiency.Second, this dissertation empirically examines the pricing performance of the B-S and constant elasticity of variance (CEV) models using the daily closing prices of55warrants traded on Shanghai and Shenzhen stock exchanges for the sample period from August2005to September2010. Empirical results demonstrate that there are no substantial differences between the B-S model and CEV model in pricing accruacy, and both the two models underprice the warrants seriously resulting in big errors. Therefore, both the B-S and CEV models are not applicable in China’s warrant market. Finally, based on the special trading mechanism in China’s stock market, we give a brief discussion on the reason of the failure of the B-S and CEV models.Third, by applying the stochastic discount factor methodology, the problem of warrant pricing when the underlying asset follows a stochastic volatility model with leverage effect (SV-L) is considered. Then, an empirical study of call warrants for trading on Shanghai and Shenzhen stock exchanges is presented. Empirical results demonstrate that the warrant prices produced by the stochastic discount factor warrant pricing model are closer to the actual market prices than the warrant prices produced by the B-S model.Fourth, the problem of warrant pricing when the underlying asset follows the GARCH diffusion model is considered, and a closed-form solution for European options is derived by means of fast Fourier transform (FFT). Monte Carlo simulations show that this closed-form solution is quite accurate and the FFT is quite efficient. Then, using data on Hang Seng Index (HSI) warrants in Hong Kong stock market, the pricing performance of the GARCH diffusion warrant pricing model is investigated. Empirical results demonstrate that the warrant prices produced by the GARCH diffusion warrant pricing model are very close to the actual market prices, and the GARCH diffusion model performs consistently better than the B-S and Heston models in terms of the absolute percentage error.Fifth, this dissertation studies the problem of American warrant pricing. By combining the least-squares Monte Carlo (LSM) method with the randomized quasi-Monte Carlo (RQMC) method, this dissertation proposes the least-squares randomized quasi-Monte Carlo (LSRQM) methods for valuing American options. Monte Carlo simulations are presented to examine the accuracy of the proposed method. Numerical results demonstrate that the LSRQM methods succeed in reducing the standard error comparing to the LSM method, and the LSRQM methods can provide more accuracy and faster convergence rate than the LSM method. Hence, the LSRQM methods are significant more efficient than the LSM method. Then, an empirical study of American-style put warrant for trading on Shanghai stock exchange is presented. Empirical results demonstrate that the warrant prices calculated by the LSRQM methods are closer to the actual market prices than the warrant prices calculated by the LSM method.