A Closed-Form GARCH Option Pricing Model

نویسندگان

  • Steven L. Heston
  • John M. Olin
  • Saikat Nandi
چکیده

This paper develops a closed-form option pricing formula for a spot asset whose variance follows a GARCH process. The model allows for correlation between returns of the spot asset and variance and also admits multiple lags in the dynamics of the GARCH process. The single-factor (one-lag) version of this model contains Heston’s (1993) stochastic volatility model as a diffusion limit and therefore unifies the discrete-time GARCH and continuous-time stochastic volatility literature of option pricing. The new model provides the first readily computed option formula for a random volatility model in which current volatility is easily estimated from historical asset prices observed at discrete intervals. Empirical analysis on S&P 500 index options shows the single-factor version of the GARCH model to be a substantial improvement over the Black-Scholes (1973) model. The GARCH model continues to substantially outperform the Black-Scholes model even when the BlackScholes model is updated every period and uses implied volatilities from option prices, while the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices. The improvement is due largely to the ability of the GARCH model to describe the correlation of volatility with spot returns. This allows the GARCH model to capture strike-price biases in the Black-Scholes model that give rise to the skew in implied volatilities in the index options market. JEL classification: G13

برای دسترسی به متن کامل این مقاله و 23 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Preference-Free Option Pricing with Path-Dependent Volatility: A Closed-Form Approach

This paper shows how one can obtain a continuous-time preference-free option pricing model with a path-dependent volatility as the limit of a discrete-time GARCH model. In particular, the continuous-time model is the limit of a discrete-time GARCH model of Heston and Nandi (1997) that allows asymmetry between returns and volatility. For the continuous-time model, one can directly compute closed...

متن کامل

An option pricing formula for the GARCH diffusion model

We derive analytically the first four conditional moments of the integrated variance implied by the GARCH diffusion process. From these moments we obtain an analytical closed-form approximation formula to price European options under the GARCH diffusion model. Using Monte Carlo simulations, we show that this approximation formula is accurate for a large set of reasonable parameters. Finally, we...

متن کامل

Dynamic Option Pricing Model Based on the Realized-GARCH-NIG Approach

In this paper, we take the advantage of high frequency data to develop option pricing model and select the Realized GARCH model to describe the volatility of assets, use NIG distribution to describe the distribution of underlying assets, and also build the Realized-GARCH-NIG model to price the option. Finally, we obtain the dynamic option pricing model based on the Realized-GARCH-NIG approach. ...

متن کامل

Option Pricing in a GARCH Framework

There is a compelling need to accurately and efficiently compute option values. Existing literature shows that models based on constant stock volatilities have been widely used in option valuation. However, stock volatilities change constantly in real life situations. The introduction of the Auto Regressive Conditional Heteroskedasticity (ARCH) model and subsequently, the Generalized Auto Regre...

متن کامل

Numerical Solution of Pricing of European Put Option with Stochastic Volatility

In this paper, European option pricing with stochastic volatility forecasted by well known GARCH model is discussed in context of Indian financial market. The data of Reliance Ltd. stockprice from 3/01/2000 to 30/03/2009 is used and resulting partial differential equation is solved byCrank-Nicolson finite difference method for various interest rates and maturity in time. Thesensitivity measures...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دسترسی به متن کامل این مقاله و 23 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997