GARCH Option Pricing Models, the CBOE VIX, and Variance Risk Premium

2013 ◽  
Vol 11 (3) ◽  
pp. 556-580 ◽  
Author(s):  
J. Hao ◽  
J. E. Zhang
Keyword(s):  
Option Pricing ◽  
Risk Premium ◽  
Pricing Models ◽  
Variance Risk Premium ◽  
Variance Risk

scholarly journals GARCH Option Pricing Models and the Variance Risk Premium

2020 ◽  
Vol 13 (3) ◽  
pp. 51
Author(s):  
Wenjun Zhang ◽  
Jin E. Zhang
Keyword(s):  
Option Pricing ◽  
Risk Premium ◽  
Empirical Estimation ◽  
Pricing Models ◽  
Variance Risk Premium ◽  
Pricing Options ◽  
Volatility Index ◽  
Risk Neutral ◽  
Local Risk ◽  
Variance Risk

In this paper, we modify Duan’s (1995) local risk-neutral valuation relationship (mLRNVR) for the GARCH option-pricing models. In our mLRNVR, the conditional variances under two measures are designed to be different and the variance process is more persistent in the risk-neutral measure than in the physical one, so that one is able to capture the variance risk premium. Empirical estimation exercises show that the GARCH option-pricing models under our mLRNVR are able to price the SPX one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use our mLRNVR when pricing options with GARCH models.

Financial Uncertainty with Ambiguity and Learning

2021 ◽  
Author(s):  
Hening Liu ◽  
Yuzhao Zhang
Keyword(s):  
Risk Premium ◽  
Regime Switching ◽  
Ambiguity Aversion ◽  
Volatility Risk ◽  
Asset Pricing Model ◽  
Variance Risk Premium ◽  
Financial Uncertainty ◽  
Empirical Relations ◽  
The Mean ◽  
Variance Risk

We examine a production-based asset pricing model with regime-switching productivity growth, learning, and ambiguity. Both the mean and volatility of the growth rate of productivity are assumed to follow a Markov chain with an unobservable state. The agent’s preferences are characterized by the generalized recursive smooth ambiguity utility function. Our calibrated benchmark model with modest risk aversion can match moments of the variance risk premium in the data and reconcile empirical relations between the risk-neutral variance and macroeconomic quantities and their respective volatilities. We show that the interplay between productivity volatility risk and ambiguity aversion is important for pricing variance risk in returns. This paper was accepted by Tomasz Piskorski, finance.

scholarly journals Variance risk premia for agricultural commodities

2019 ◽  
Vol 79 (3) ◽  
pp. 286-303
Author(s):  
Wenwen Xi ◽  
Dermot Hayes ◽  
Sergio Horacio Lence
Keyword(s):  
Risk Premium ◽  
Price Volatility ◽  
Risk Premia ◽  
Content Type ◽  
Risk Premiums ◽  
Variance Risk Premium ◽  
Revenue Insurance ◽  
Risk Neutral ◽  
Variance Risk ◽  
Practical Implications

Purpose The purpose of this paper is to study the variance risk premium in corn and soybean markets, where the variance risk premium is defined as the difference between the historical realized variance and the corresponding risk-neutral expected variance. Design/methodology/approach The authors compute variance risk premiums using historical derivatives data. The authors use regression analysis and time series econometrics methods, including EGARCH and the Kalman filter, to analyze variance risk premiums. Findings There are moderate commonalities in variance within the agricultural sector, but fairly weak commonalities between the agricultural and the equity sectors. Corn and soybean variance risk premia in dollar terms are time-varying and correlated with the risk-neutral expected variance. In contrast, agricultural commodity variance risk premia in log return terms are more likely to be constant and less correlated with the log risk-neutral expected variance. Variance and price (return) risk premia in agricultural markets are weakly correlated, and the correlation depends on the sign of the returns in the underlying commodity. Practical implications Commodity variance (i.e. volatility) risk cannot be hedged using futures markets. The results have practical implications for US crop insurance programs because the implied volatilities from the relevant options markets are used to estimate the price volatility factors used to generate premia for revenue insurance products such as “Revenue Protection” and “Revenue Protection with Harvest Price Exclusion.” The variance risk premia found implies that revenue insurance premia are overpriced. Originality/value The empirical results suggest that the implied volatilities in corn and soybean futures market overestimate true expected volatility by approximately 15 percent. This has implications for derivative products, such as revenue insurance, that use these implied volatilities to calculate fair premia.

scholarly journals Option-Based Estimation of the Price of Coskewness and Cokurtosis Risk

2020 ◽  
pp. 1-27
Author(s):  
Peter Christoffersen ◽  
Mathieu Fournier ◽  
Kris Jacobs ◽  
Mehdi Karoui
Keyword(s):  
Risk Premium ◽  
Risk Premia ◽  
Factor Models ◽  
Option Prices ◽  
Variance Risk Premium ◽  
Market Return ◽  
Price Of Risk ◽  
Variance Risk ◽  
Index Option

Abstract We show that the prices of risk for factors that are nonlinear in the market return can be obtained using index option prices. The price of coskewness risk corresponds to the market variance risk premium, and the price of cokurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An analysis of factor models with coskewness risk indicates that the new estimates of the price of risk improve the models’ performance compared with regression-based estimates.

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