ECONOMETRICS

Econometrics



Econometrics

Part A

Introduction

The importance of energy markets has increased with the development of futures and options markets, and with the always-important impact of energy on the economy. In this paper, we seek an in-depth understanding of priced volatility in the energy markets, as well as quantitatively displaying the mirror-image aspect of the energy and equity markets: Whereas prices and volatilities are negatively correlated in the equity markets, they tend to display a positive correlation in the energy markets. Because of this positive correlation, computing a negative market price of volatility risk in energy markets may imply a negative market price of commodity risk in the energy markets and consequently an upward-bias of energy futures contracts prices relative to expected spot prices.

The volatility risk premium

The current state of the literature on volatility risk premium has focused on equity markets, in part due to the prevalence of option data on indices such as the S&P 500. Much of the attention paid to energy markets focuses on modeling and estimating convenience yields. The general findings suggest that convenience yields are positive, since futures prices are generally below spot, are negatively correlated with inventories, and tend to be time-varying. While estimation of the convenience yield is typically conducted using spot and futures prices, estimating the market price of volatility risk needs be derived from information in option prices. With increased access to energy option data, estimation of the volatility risk premium is now more reliable. By using the realized volatility of the futures contract price, and implied volatility from the options on those futures, the volatility risk premium can be inferred.

For equities, the consensus of works such as Bakshi and Kapadia, 2003 G. Bakshi and N. Kapadia, Delta-hedged gains and the negative market volatility risk premium, find that the market price of volatility risk is negative. Several authors, such as Pan (2002) and more recently, Broadie et al. (2007), disagree with the marginal impact of this risk parameter, noting that empirically disentangling multiple risk premiums is problematic. Our intuition regarding the sign of the market price of volatility risk is informed in part by the notion that options are purchased as hedges against significant declines in the equity market, and buyers of the options are willing to pay a premium for such downside protection. In addition to the high Sharpe ratios in trading option, pointed out by Bates (2000) and (Eraker, 2004) and (Jackwerth and Rubinstein, 1996) have also suggested that at-the-money (ATM) implied volatilities are systematically higher than realized volatilities, a phenomenon that clearly be explained by a negative volatility risk premium.

While implied volatilities are higher than realized volatilities in energy markets, too, the dynamics of the energy markets differ from those of equity markets in specific ways:

1. Higher market prices tend to coincide with higher volatility.

2. Beta coefficients tend to be negative for commodities markets.

3. There is a significant term-structure of volatility and (at least in some markets) seasonality for energy prices.

In the presence of these major differences we show that the market ...