Jin-Chuan Duan

Augmented GARCH (p,q) process and its diffusion limit

Abstract A family of parametric GARCH models, defined in terms of an auxiliary process and referred to as the augmented GARCH process, is proposed. The strict stationarity of the augmented GARCH process is characterized and this process is shown to contain many existing parametric GARCH models. The augmented GARCH process can serve as a general alternative for Lagrange Multiplier test of many existing GARCH specifications. The diffusion limit of the augmented GARCH process is shown to contain many bivariate diffusion processes that are commonly used for modeling stochastic volatility in the finance literature. This convergence result generalizes that of Nelson (1990a) to cover a substantially larger class of GARCH (1,1) models and also extends to the GARCH ( p , q ) specification. The augmented GARCH process can be used as a direct approximation to the stochastic volatility models, or as the score generator in the efficient method of moments (Gallant and Tauchen, 1996) estimation of these models.

Estimating and Testing Exponential Affine Term Structure Models by Kalman Filter

This paper proposes a unified state-space formulation for parameter estimation of exponential-affine term structure models. The proposed method uses an approximate linear Kalman filter which only requires specifying the conditional mean and variance of the system in an approximate sense. The method allows for measurement errors in the observed yields to maturity, and can simultaneously deal with many yields on bonds with different maturities. An empirical analysis of two special cases of this general class of model is carried out: the Gaussian case (Vasicek 1977) and the non-Gaussian case (Cox Ingersoll and Ross 1985 and Chen and Scott 1992). Our test results indicate a strong rejection of these two cases. A Monte Carlo study indicates that the procedure is reliable for moderate sample sizes.

American option pricing under GARCH by a Markov chain approximation

Abstract We propose a numerical method for valuing American options in general and for the GARCH option pricing model in particular. The method is based on approximating the underlying asset price process by a finite-state, time-homogeneous Markov chain. Since the Markov transition probability matrix can be derived analytically, the price of an American option can be computed by simple matrix operations. The Markov transition probability matrix is typically sparse. The use of a sparse matrix representation can substantially increase the dimension of the Markov chain to obtain better numerical results. The Markov chain method works well for the GARCH option pricing framework, and it serves as an alternative to the existing numerical methods for the valuation of American options in other pricing settings. We provide a convergence proof for the Markov chain method and analyze its numerical performance for the Black–Scholes (1973) and GARCH option pricing models.

Option pricing under regime switching

Abstract This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357–84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.

Fixed-rate deposit insurance and risk-shifting behavior at commercial banks

Abstract Fixed-rate deposit insurance is thought to provide banks with an incentive to shift risk to the FDIC, thereby expropriating wealth. Banks can achieve these wealth transfers by increasing their overall risk and thus increasing the actuarial value of the deposit insurance. In this paper, the risk-shifting hypothesis is tested on a sample of US banks. An option-based methodology is used to price each banks actuarial liability to the FDIC. Statistical tests are then conducted to determine if banks have been successful in manipulating risk in such a way as to increase these liabilities. The results suggest that risk-shifting is not widespread, although there are notable exceptions.

APPROXIMATING GARCH‐JUMP MODELS, JUMP‐DIFFUSION PROCESSES, AND OPTION PRICING

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset prices and volatilities. We extend theory developed by Nelson (1990) and Duan (1997) by considering the limiting models for our approximating GARCH Jump process. Limiting cases of our processes consist of models where both asset price and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of a few GARCH models to their continuous time limits is evaluated and the benefits of the models explored.

Pricing Hang Seng Index options around the Asian financial crisis – A GARCH approach

Abstract This paper investigates how well the Hang Seng Index options, the most important class of option contracts traded in Hong Kong, are priced using the GARCH approach. We calibrated the GARCH parameters using the call and put option data and used them to price options in the subsequent weeks. We found the GARCH model performs very well in comparison with the Black–Scholes model even after allowing for a smile/smirk adjustment. Its superior performance was also evident both before and during the recent Asian financial turmoil.

Deposit insurance and bank interest rate risk: Pricing and regulatory implications

Abstract The linkage between the interest rate risk exposure of banks and the liabilities of a deposit insuring agency is not well understood. In this paper, a model is developed to evaluate the interest rate risk exposure of both deposit taking institutions and deposit insuring agents when bank equity has limited liability and interest rates are stochastic. Based on a sample of U.S. banks, empirical results are presented for the interest rate risk exposure of banks and its impact on the liabilities of the FDIC.

Pricing Discretely Monitored Barrier Options by a Markov Chain

Barrier options have become commonplace in the option market, and a variety of other financial contracts may also be thought of in terms of barrier options. But the existence of a price barrier can significantly complicate the option valuation problem when volatility is time-varying, or the barrier itself moves over time, or the barrier is only monitored at discrete intervals. In this article, Duan et al. present a new Markov chain technology for pricing barrier options that readily handles all of these problems. Out-and-in options can be valued within their framework even when volatility follows a GARCH process and a discretely monitored time-varying barrier is present.

Volatility and maturity effects in the Nikkei index futures

Many financial data series are found to exhibit stochastic volatility. Some of these time series are constructed from contracts with time‐varying maturities. In this paper, we focus on index futures, an important subclass of such time series. We propose a bivariate GARCH model with the maturity effect to describe the joint dynamics of the spot index and the futures‐spot basis. The setup makes it possible to examine the Samuelson effect as well as to compare the hedge ratios under scenarios with and without the maturity effect. The Nikkei‐225 index and its futures are used in our empirical analysis. Contrary to the Samuelson effect, we find that the volatility of the futures price decreases when the contract is closer to its maturity. We also apply our model to futures hedging, and find that both the optimal hedge ratio and the hedging effectiveness critically depend on both the maturity and GARCH effects.