The Price of the Smile and Variance Risk Premia

2020 ◽  
Author(s):  
Peter H. Gruber ◽  
Claudio Tebaldi ◽  
Fabio Trojani
Keyword(s):  
Term Structure ◽  
Risk Premium ◽  
Implied Volatility ◽  
Risk Premia ◽  
State Variables ◽  
State Spaces ◽  
State Process ◽  
Joint Dynamics ◽  
Variance Risk ◽  
Implied Volatility Surfaces

Using a new specification of multifactor volatility, we estimate the hidden risk factors spanning S&P 500 index (SPX) implied volatility surfaces and the risk premia of volatility-sensitive payoffs. SPX implied volatility surfaces are well-explained by three dependent state variables reflecting (i) short- and long-term implied volatility risks and (ii) short-term implied skewness risk. The more persistent volatility factor and the skewness factor support a downward sloping term structure of variance risk premia in normal times, whereas the most transient volatility factor accounts for an upward sloping term structure in periods of distress. Our volatility specification based on a matrix state process is instrumental to obtaining a tractable and flexible model for the joint dynamics of returns and volatilities, which improves pricing performance and risk premium modeling with respect to recent three-factor specifications based on standard state spaces. This paper was accepted by Gustavo Manso, finance.

scholarly journals Inflation Risk Premia, Yield Volatility, and Macro Factors

2018 ◽  
Vol 17 (3) ◽  
pp. 397-431 ◽  
Author(s):  
Andrea Berardi ◽  
Alberto Plazzi
Keyword(s):  
Term Structure ◽  
Risk Premium ◽  
Implied Volatility ◽  
Risk Premia ◽  
Output Growth ◽  
Inflation Risk ◽  
Variance Risk Premium ◽  
Real Risk ◽  
Variance Risk ◽  
Inflation Risk Premia

Abstract We incorporate a latent stochastic volatility factor and macroeconomic expectations in an affine model for the term structure of nominal and real rates. We estimate the model over 1999–2016 on U.S. data for nominal and TIPS yields, the realized and implied volatility of T-bonds, and survey forecasts of GDP growth and inflation. We find relatively stable inflation risk premia averaging at 40 basis points at the long-end, and which are strongly related to the volatility factor and conditional mean of output growth. We also document real risk premia that turn negative in the post-crisis period, and a non-negligible variance risk premium.

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.

The term structure of equity and variance risk premia

2020 ◽  
Vol 219 (2) ◽  
pp. 204-230 ◽  
Author(s):  
Yacine Aït-Sahalia ◽  
Mustafa Karaman ◽  
Loriano Mancini
Keyword(s):  
Term Structure ◽  
Risk Premia ◽  
Variance Risk

scholarly journals On the Timing and Pricing of Dividends: Comment

2016 ◽  
Vol 106 (10) ◽  
pp. 3185-3223 ◽  
Author(s):  
Florian Schulz
Keyword(s):  
Term Structure ◽  
Risk Premium ◽  
Risk Premia ◽  
Equity Returns ◽  
Equity Risk Premium ◽  
Short Term ◽  
Equity Risk ◽  
Market Portfolio ◽  
Show Evidence

I present novel empirical evidence on the term structure of the equity risk premium. In contrast to previous research that documented high discount rates for the short-term component of the market portfolio, I show evidence for an unconditionally flat term structure of equity risk premia. The tension with previous literature arises largely as a result of differential treatments of heterogeneous investment taxes, manifested in micro evidence on abnormal equity returns on ex-dividend days, and liquidity. The results not only help resolve an important recent “puzzle” but provide further important insights on the role of investment taxes in asset pricing. (JEL G11, G12, G35)

Risk Premia and the VIX Term Structure

2017 ◽  
Vol 52 (6) ◽  
pp. 2461-2490 ◽  
Author(s):  
Travis L. Johnson
Keyword(s):  
Term Structure ◽  
Principal Component ◽  
Risk Premia ◽  
Expectations Hypothesis ◽  
Variance Swaps ◽  
Volatility Index ◽  
Asset Pricing Models ◽  
Vix Futures ◽  
Synthetic Standard ◽  
Variance Risk

The shape of the Chicago Board Options Exchange Volatility Index (VIX) term structure conveys information about the price of variance risk rather than expected changes in the VIX, a rejection of the expectations hypothesis. The second principal component, SLOPE, summarizes nearly all this information, predicting the excess returns of synthetic Standard & Poor’s (S&P) 500 variance swaps, VIX futures, and S&P 500 straddles for all maturities and to the exclusion of the rest of the term structure. SLOPE’s predictability is incremental to other proxies for the conditional variance risk premia, economically significant, and inconsistent with standard asset pricing models.

WEIGHTED MONTE CARLO: A NEW TECHNIQUE FOR CALIBRATING ASSET-PRICING MODELS

2001 ◽  
Vol 04 (01) ◽  
pp. 91-119 ◽  
Author(s):  
MARCO AVELLANEDA ◽  
ROBERT BUFF ◽  
CRAIG FRIEDMAN ◽  
NICOLAS GRANDECHAMP ◽  
LUKASZ KRUK ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Term Structure ◽  
Implied Volatility ◽  
Empirical Measure ◽  
Forward Rate ◽  
Exotic Options ◽  
Finite Sample ◽  
Market Prices ◽  
A New Technique ◽  
Implied Volatility Surfaces

A general approach for calibrating Monte Carlo models to the market prices of benchmark securities is presented. Starting from a given model for market dynamics (price diffusion, rate diffusion, etc.), the algorithm corrects price-misspecifications and finite-sample effects in the simulation by assigning "probability weights" to the simulated paths. The choice of weights is done by minimizing the Kullback–Leibler relative entropy distance of the posterior measure to the empirical measure. The resulting ensemble prices the given set of benchmark instruments exactly or in the sense of least-squares. We discuss pricing and hedging in the context of these weighted Monte Carlo models. A significant reduction of variance is demonstrated theoretically as well as numerically. Concrete applications to the calibration of stochastic volatility models and term-structure models with up to 40 benchmark instruments are presented. The construction of implied volatility surfaces and forward-rate curves and the pricing and hedging of exotic options are investigated through several examples.

The Variance Swaps based on KOSPI200 Index and the Term Structure of Variance Risk Premium

2013 ◽  
Vol 21 (4) ◽  
pp. 435-463
Author(s):  
Young Ho Eom ◽  
Woon Wook Jang
Keyword(s):  
Risk Factors ◽  
Term Structure ◽  
Risk Premium ◽  
Risk Averse ◽  
Realized Variance ◽  
Over The Counter ◽  
Variance Swaps ◽  
Variance Swap ◽  
Variance Risk Premium ◽  
Variance Risk

This study examines whether the variance risk is a priced risk factor in Korea using the over-the-counter variance swap quotes and realized variance data. We also study the term structure of variance risk premium. The empirical results show that the model with 2 stochastic variance risk factors with jumps in return is required to fit the variance swap and realized variance data. The analyses with the estimated models suggest that the variance risk premium in Korea are highly negative and the size of the premium increase with the maturities, meaning that risk averse investors in Korea are willing to pay a premium to hedge variance risk.

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