A Note on Stochastic Volatility , GARCHmodels , and Hyperbolic

نویسنده

  • Stefan R. Jaschke
چکیده

We establish a relation between stochastic volatility models and the class of generalized hyperbolic distributions. These distributions have been found to t exceptionally well to the empirical distribution of stock returns. We review the background of hyper-bolic distributions and prove stationary distributions of certain GARCH-type models to be generalized hyperbolic.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Unifying the Bgm and Sabr Models: a Short Ride in Hyperbolic Geometry

In this short note, using our geometric method introduced in a previous paper [12] and initiated by [4], we derive an asymptotic swaption implied volatility at the first-order for a general stochastic volatility Libor Market Model. This formula is useful to quickly calibrate a model to a full swaption matrix. We apply this formula to a specific model where the forward rates are assumed to follo...

متن کامل

Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications

In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...

متن کامل

Simulating Exchange Rate Volatility in Iran Using Stochastic Differential ‎Equations‎

‎The main purpose of this paper is to analyze the exchange rate volatility in Iran in the time period between 2011/11/27 and 2017/02/25 on a daily basis. As a tradable asset and as an important and effective economic  variable, exchange rate plays a decisive role in the economy of a country. In a successful economic management, the modeling and prediction of the exchange rate volatility is esse...

متن کامل

Risk Management Based on Stochastic Volatility

Risk management approaches that do not incorporate randomly changing volatility tend to underor overestimate the risk depending on current market conditions. We show how some popular stochastic volatility models in combination with the hyperbolic model introduced in Eberlein and Keller (1995) can be applied quite easily for risk management purposes. Moreover, we compare their relative performan...

متن کامل

Volatility and Quantile Forecasts by Realized Stochastic Volatility Models with Generalized Hyperbolic Distribution

The predictive performance of the realized stochastic volatility model of Takahashi, Omori, and Watanabe (2009), which incorporates the asymmetric stochastic volatility model with the realized volatility, is investigated. Considering well known characteristics of financial returns, heavy tail and negative skewness, the model is extended by employing a wider class distribution, the generalized h...

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 دانلود متن کامل این مقاله و بیش از 32 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