Abstract
Investors’ decisions on capital markets depend on their anticipation and preferences about risk, and volatility is one of the most common measures of risk. This paper proposes a method of estimating the market price of volatility risk by incorporating both conditional heteroscedasticity and nonlinear effects in market returns, while accounting for asymmetric shocks. We develop a model that allows dynamic risk premiums for the underlying asset and for the volatility of the asset under the physical measure. Specifically, a nonlinear in mean time series model combining the asymmetric autoregressive conditional heteroscedastic model with leverage (NGARCH) is adapted for modeling return dynamics. The local risk-neutral valuation relationship is used to model investors’ preferences of volatility risk. The transition probabilities governing the evolution of the price of the underlying asset are adjusted for investors’ attitude towards risk, presenting the asset returns as a function of the risk premium. Numerical studies on asset return data show the significance of market shocks and levels of asymmetry in pricing the volatility risk. Estimated premiums could be used in option pricing models, turning options markets into volatility trading markets, and in measuring reactions to market shocks.
Highlights
Financial derivatives and instruments for risk reduction provide a practical means to hedge and manage the risk from trading financial securities
Using both option prices and returns under the risk-neutral as well as the physical probability measure, the authors of [16] evaluated different GARCH models out-of-sample. Their analysis favors a relatively parsimonious model that, besides volatility clustering, only allows for a standard leverage effect. We benefit from this idea and design a discrete stochastic volatility model for pricing the volatility risk premium, accounting for the fact that level-depending volatility is an important feature observed in option markets as well as in the underlying prices
We introduce a new variant of the discrete stochastic volatility nonlinear asymmetric GARCH model (NGARCH)
Summary
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