Search

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. (C) 2001 Elsevier Science BN. All rights reserved.

Monte Carlo simulation is commonly used for computing prices of derivative securities when an analytical solution does not exist. Recently, a new simulation technique known as empirical martingale simulation (EMS) has been proposed by Duan and Simonato (1998) as a way of improving simulation accuracy. EMS has one drawback however. Because of the dependency among sample paths created by the EMS adjustment, the standard error of the price estimate is not readily available from using one simulation sample. In this paper, we develop a scheme to estimate the EMS accuracy. The EMS price estimator is first shown to have an asymptotically normal distribution. Through a simulation study, we then find that the asymptotic normal distribution serves as a good approximation for samples consisting of as few as 500 simulation paths.

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. (C) 2001 Elsevier Science BN. All rights reserved.

Monte Carlo simulation is commonly used for computing prices of derivative securities when an analytical solution does not exist. Recently, a new simulation technique known as empirical martingale simulation (EMS) has been proposed by Duan and Simonato (1998) as a way of improving simulation accuracy. EMS has one drawback however. Because of the dependency among sample paths created by the EMS adjustment, the standard error of the price estimate is not readily available from using one simulation sample. In this paper, we develop a scheme to estimate the EMS accuracy. The EMS price estimator is first shown to have an asymptotically normal distribution. Through a simulation study, we then find that the asymptotic normal distribution serves as a good approximation for samples consisting of as few as 500 simulation paths.

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. (C) 2001 Elsevier Science B.V. All rights reserved.

Monte Carlo simulation is commonly used for computing prices of derivative securities when an analytical solution does not exist. Recently, a new simulation technique known as empirical martingale simulation (EMS) has been proposed by Duan and Simonato (1998) as a way of improving simulation accuracy. EMS has one drawback however. Because of the dependency among sample paths created by the EMS adjustment, the standard error of the price estimate is not readily available from using one simulation sample. In this paper, we develop a scheme to estimate the EMS accuracy. The EMS price estimator is first shown to have an asymptotically normal distribution. Through a simulation study, we then find that the asymptotic normal distribution serves as a good approximation for samples consisting of as few as 500 simulation paths.

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. (C) 2001 Elsevier Science BN. All rights reserved.

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. (C) 2001 Elsevier Science B.V. All rights reserved.

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. (C) 1999 John Wiley & Sons, Inc.

We propose a multiperiod deposit insurance pricing model that simultaneously incorporates the capital standard and the possibility of forbearance. The model employs the recently developed GARCH option pricing technique in determining the deposit insurance value. Our model offers two distinctive advantages. First, it explicitly considers the implications of the strict enforcement on capital standard as stipulated in FDIC Improvement Act of 1991. Second, the use of the GARCH model;allows us to capture many robust features exhibited by financial asset returns. By the GARCH option pricing theory, the value of a contingent claim is a function of the asset risk premium. This unique feature is found to be prominent in determining the bank's deposit insurance value. We also examine the effects of capital forbearance and moral hazard behavior in this multiperiod deposit insurance setting. (C) 1999 Elsevier Science B.V. All rights reserved.

We propose a multiperiod deposit insurance pricing model that simultaneously incorporates the capital standard and the possibility of forbearance. The model employs the recently developed GARCH option pricing technique in determining the deposit insurance value. Our model offers two distinctive advantages. First, it explicitly considers the implications of the strict enforcement on capital standard as stipulated in FDIC Improvement Act of 1991. Second, the use of the GARCH model;allows us to capture many robust features exhibited by financial asset returns. By the GARCH option pricing theory, the value of a contingent claim is a function of the asset risk premium. This unique feature is found to be prominent in determining the bank's deposit insurance value. We also examine the effects of capital forbearance and moral hazard behavior in this multiperiod deposit insurance setting. (C) 1999 Elsevier Science B.V. All rights reserved.

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. (C) 1999 John Wiley & Sons, Inc.

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. (C) 1999 John Wiley & Sons, Inc.

We propose a multiperiod deposit insurance pricing model that simultaneously incorporates the capital standard and the possibility of forbearance. The model employs the recently developed GARCH option pricing technique in determining the deposit insurance value. Our model offers two distinctive advantages. First, it explicitly considers the implications of the strict enforcement on capital standard as stipulated in FDIC Improvement Act of 1991. Second, the use of the GARCH model;allows us to capture many robust features exhibited by financial asset returns. By the GARCH option pricing theory, the value of a contingent claim is a function of the asset risk premium. This unique feature is found to be prominent in determining the bank's deposit insurance value. We also examine the effects of capital forbearance and moral hazard behavior in this multiperiod deposit insurance setting. (C) 1999 Elsevier Science B.V. All rights reserved.

This paper proposes a simple modification to the standard Monte Carlo simulation procedure for computing the prices of derivative securities. The modification imposes the martingale property on the simulated sample paths of the underlying asset price. This procedure is referred to as the empirical martingale simulation (EMS). The EMS ensures that the price estimated by simulation satisfies the rational option pricing bounds. The EMS yields a substantial error reduction for the price estimate and can be easily coupled with the standard variance reduction methods. Simulation studies are conducted for European and Asian call options using both the Black and Scholes and GARCH option pricing frameworks. The results indicate that the EMS yields substantial variance reduction particularly for in- and at-the-money or longer-maturity options. The option price estimate based on the EMS is found to exhibit a minor small-sample bias only in few occasions. An analysis of the trade-off between computing time and price accuracy reveals that the EMS dominates the conventional simulation methods.

This paper proposes a simple modification to the standard Monte Carlo simulation procedure for computing the prices of derivative securities. The modification imposes the martingale property on the simulated sample paths of the underlying asset price. This procedure is referred to as the empirical martingale simulation (EMS). The EMS ensures that the price estimated by simulation satisfies the rational option pricing bounds. The EMS yields a substantial error reduction for the price estimate and can be easily coupled with the standard variance reduction methods. Simulation studies are conducted for European and Asian call options using both the Black and Scholes and GARCH option pricing frameworks. The results indicate that the EMS yields substantial variance reduction particularly for in- and at-the-money or longer-maturity options. The option price estimate based on the EMS is found to exhibit a minor small-sample bias only in few occasions. An analysis of the trade-off between computing time and price accuracy reveals that the EMS dominates the conventional simulation methods.

This paper proposes a simple modification to the standard Monte Carlo simulation procedure for computing the prices of derivative securities. The modification imposes the martingale property on the simulated sample paths of the underlying asset price. This procedure is referred to as the empirical martingale simulation (EMS). The EMS ensures that the price estimated by simulation satisfies the rational option pricing bounds. The EMS yields a substantial error reduction for the price estimate and can be easily coupled with the standard variance reduction methods. Simulation studies are conducted for European and Asian call options using both the Black and Scholes and GARCH option pricing frameworks. The results indicate that the EMS yields substantial variance reduction particularly for in- and at-the-money or longer-maturity options. The option price estimate based on the EMS is found to exhibit a minor small-sample bias only in few occasions. An analysis of the trade-off between computing time and price accuracy reveals that the EMS dominates the conventional simulation methods.

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.

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.

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.

In this article, we assume a fractionally integrated GARCH dynamic for the aggregate consumption growth rate and use the Euler equation to derive a long-memory equilibrium interest rate process. This simple model links together two strains of seemingly unrelated empirical findings: the long-memory property exhibited by interest rates on the one hand and the fractionally integrated volatility dynamic of market portfolio returns on the other.

In this article, we assume a fractionally integrated GARCH dynamic for the aggregate consumption growth rate and use the Euler equation to derive a long-memory equilibrium interest rate process. This simple model links together two strains of seemingly unrelated empirical findings: the long-memory property exhibited by interest rates on the one hand and the fractionally integrated volatility dynamic of market portfolio returns on the other.

In this article, we assume a fractionally integrated GARCH dynamic for the aggregate consumption growth rate and use the Euler equation to derive a long-memory equilibrium interest rate process. This simple model links together two strains of seemingly unrelated empirical findings: the long-memory property exhibited by interest rates on the one hand and the fractionally integrated volatility dynamic of market portfolio returns on the other.