Time‐varying market price of risk in the crude oil futures market

Abstract

In this study, a three‐factor model of crude oil prices is estimated, which incorporates a time‐varying market price of risk. The model is able to accurately capture the term structure of futures prices with evidence suggesting that risk premiums in the crude oil market are time‐varying. Using the cross‐section of futures prices, we estimate a time‐series of the market price of risk in the crude oil market implied by the model. We find that the risk premiums in the crude oil market are driven by the same risk factors as equity and bond markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:779–807, 2011

Commodity derivative valuation under a factor model with time-varying market prices of risk

“…Finally, as stated above, there have been several papers that have estimated factor models allowing for time-varying market prices of risk (Casassus and Collin-Dufresne 2005;Trolle and Schwartz 2009;Bhar and Lee 2011;Casassus et al 2013). However, these papers do not test the importance of time-varying market prices o f risk on the valuation of exchange-traded options, compared to the constant market prices of risk case.…”

“…Specifically, we show the importance of allowing for time-varying market prices of risk in valuing a set of market traded commodity options. As stated in the Introduction, there have been several papers that have estimated factor models allowing for time-varying market prices of risk (Casassus and Collin-Dufresne 2005;Trolle and Schwartz 2009;Bhar and Lee 2011;. However, they do not analyze the effect of time-varying market prices of risk, compared to the constant case, from the point of view of the valuation of exchange-traded options.…”

“…However, they do not compare the effects of time-varying and constant market prices of risk from the point of view of option valuation. Bhar and Lee (2011) propose a three-factor model for crude oil prices with time-varying market prices of risk. They apply their model to the valuation of crude oil futures prices, but they do not test the effect of time-varying market prices of risk on option pricing.…”

Measuring bias in a term-structure model of commodity prices through the comparison of simultaneous and sequential estimation

“…The standard approach in this literature is to specify the stochastic dynamics of an underlying asset, usually the spot price of the commodity under investigation, by a series of stochastic differential equations, and derive from the suggested model valuation formulas of various derivative contracts whose payoff depends on the value of the underlying asset realized at the contract maturity date [7]. 1 Recent advancements in this modeling approach have been attained through increasing the number of state variables to specify the stochastic dynamics of the underlying spot price and/or stipulating more complex stochastic process of each state variable. These flexible models generally exhibit better fit to the observed price data.…”

Multi-factor models and the risk premiums: a simulation study

“…See for example Schwartz and Smith (2000), Wilkens and Wimschulte (2007), Cartea and Williams (2008), Bhar and Lee (2011) and Nomikos and Soldatos (2010). If the Kalman filter is applied, standard deviations of parameter estimates are readily available.…”