Stochastic Convenience Yield and the Pricing of Oil Contingent Claims
TL;DR: In this article, the authors developed and empirically tested a two-factor model for pricing financial and real assets contingent on the price of oil and applied it to determine the present values of one barrel of oil deliverable in one to ten years time.
Abstract: This paper develops and empirically tests a two-factor model for pricing financial and real assets contingent on the price of oil. The factors are the spot price of oil and the instantaneous convenience yield. The parameters of the model are estimated using weekly oil futures contract prices from January 1984 to November 1988, and the model's performance is assessed out of sample by valuing futures contracts over the period November 1988 to May 1989. Finally, the model is applied to determine the present values of one barrel of oil deliverable in one to ten years time.
Citations
More filters
TL;DR: In this article, the authors compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets.
Abstract: In this article we compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets. The first model is a simple one-factor model 'in which the logarithm of the spot price of the commodity is assumed to follow a mean reverting process. The second model takes into account a second stochastic factor, the convenience yield of the commodity, which is assumed to follow a mean reverting process. Finally, the third model also includes stochastic interest rates. The Kalman filter methodology is used to estimate the parameters of the three models for two commercial commodities, copper and oil, and one precious metal, gold. The analysis reveals strong mean reversion in the commercial commodity prices. Using the estimated parameters, we analyze the implications of the models for the term structure of futures prices and volatilities beyond the observed contracts, and for hedging contracts for future delivery. Finally, we analyze the implications of the models for capital budgeting decisions. THE STOCHASTIC BEHAVIOR OF commodity prices plays a central role in the models for valuing financial contingent claims on the commodity, and in the procedures for evaluating investments to extract or produce the commodity. Earlier studies, by assuming that interest rates and convenience yields are constant allowed for a straight forward extension of the procedures developed for common stock option pricing to the valuation of financial and real commodity contingent claims. The assumption, however, is clearly not very satisfactory since it implies that the volatility of future prices is equal to the volatility of spot prices, and that the distribution of future spot prices under the equivalent martingale measure has a variance that increases without bound as the horizon increases. In an equilibrium setting we would expect that when prices are relatively high, supply will increase since higher cost producers of the commodity will enter the market putting a downward pressure on prices. Conversely, when prices are relatively low, supply will decrease since some of
2,159 citations
TL;DR: In this article, the authors compare a variety of continuous-time models of the short-term riskless rate using the Generalized Method of Moments and find that the most successful models are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rates.
Abstract: We estimate and compare a variety of continuous-time models of the short-term riskless rate using the Generalized Method of Moments. We find that the most successful models in capturing the dynamics of the short-term interest rate are those that allow the volatility of interest rate changes to be highly sensitive to the level of the riskless rate. A number of well-known models perform poorly in the comparisons because of their implicit restrictions on term structure volatility. We show that these results have important implications for the use of different term structure models in valuing interest rate contingent claims and in hedging interest rate risk.
1,853 citations
Cites background from "Stochastic Convenience Yield and th..."
...Examples include Jamshidian (1989) and Gibson and Schwartz (1990)....
[...]
TL;DR: The authors developed a two-factor model of commodity prices that allows meanreversion in short-term prices and uncertainty in the equilibrium level to which prices revert, which can be estimated from spot and futures prices.
Abstract: In this article, we develop a two-factor model of commodity prices that allows meanreversion in short-term prices and uncertainty in the equilibrium level to which prices revert. Although these two factors are not directly observable, they may be estimated from spot and futures prices. Intuitively, movements in prices for long-maturity futures contracts provide information about the equilibrium price level, and differences between the prices for the short-and long-term contracts provide information about short-term variations in prices. We show that, although this model does not explicitly consider changes in convenience yields over time, this short-term/long-term model is equivalent to the stochastic convenience yield model developed in Gibson and Schwartz 1990. We estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil-linked assets to demonstrate its use and some of its advantages over the Gibson-Schwartz model.
1,129 citations
Cites background or methods from "Stochastic Convenience Yield and th..."
...Yet, as mentioned in the introduction, the short-term/long-term model is equivalent to the stochastic convenience yield model developed in Gibson and Schwartz (1990) in that the factors in each model can be represented as linear combinations of the factors in the other....
[...]
...Yet, as mentioned in the introduction, the short-term/long-term model is equivalent to the stochastic convenience yield model developed in Gibson and Schwartz (1990) in that the factors in each model can be represented as linear combinations of the factors in the other. To show this equivalence, we first briefly describe the Gibson-Schwartz model. Adopting the notation of Schwartz (1997), we let t denote the time-t convenience yield and let X t denote the log of the time-t current spot price....
[...]
...We show that, although this model does not explicitly consider changes in convenience yields over time, this short-term/long-term model is equivalent to the stochastic convenience yield model developed in Gibson and Schwartz (1990). We estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil-linked assets to demonstrate its use and some of its advantages over the Gibson-Schwartz model....
[...]
...Although this short-term/longterm model makes no mention of convenience yields, the model turns out to be exactly equivalent to the stochastic convenience yield model of Gibson and Schwartz (1990) with the short-term price deviation being a linear function of the instantaneous convenience yield....
[...]
Posted Content•
TL;DR: The authors examined the information transmission mechanism linking oil futures with stock prices, where they examined the lead and lag cross-correlations of returns in one market with the others and investigated the dynamic interactions between oil futures prices traded on the New York Mercantile Exchange (NYMEX) and US stock prices.
Abstract: This study analyzes the information transmission mechanism linking oil futures with stock prices, where we examine the lead and lag cross-correlations of returns in one market with the others We investigate the dynamic interactions between oil futures prices traded on the New York Mercantile Exchange (NYMEX) and US stock prices, which allows us to examine the effects of energy shocks on financial markets In particular, we examine the extent to which these markets are contemporaneously correlated, with particular attention paid to the association of oil price indexes with the SP 12 major industry stock price indices and 3 individual oil company stock price series We also examine the extent to which price changes or returns in one market dynamically lead returns in the others and whether volatility spillover effects exist across these markets Using VAR model estimates for various time series of returns we find that petroleum industry stock index and our three oil company stocks are the only series where we can reject the null hypothesis that oil futures do not lead Treasury Bill rates and stock returns, while we can reject the hypothesis that oil futures lag these other two series Finally, the return volatility evidence for oil futures leading individual oil company stocks is much weaker than is the evidence for returns themselves
940 citations
Cites background from "Stochastic Convenience Yield and th..."
...Gibson and Schwartz (1990) address the pricing of crude oil futures....
[...]
TL;DR: This paper examined the information transmission mechanism linking oil futures with stock prices, where they examined the lead and lag cross-correlations of returns in one market with the others and whether volatility spillover effects exist across these markets.
Abstract: This study analyzes the information transmission mechanism linking oil futures with stock prices, where we examine the lead and lag cross-correlations of returns in one market with the others. We investigate the dynamic interactions between oil futures prices traded on the New York Mercantile Exchange (NYMEX) and U.S. stock prices, which allows us to examine the effects of energy shocks on financial markets. In particular, we examine the extent to which these markets are contemporaneously correlated, with particular attention paid to the association of oil price indexes with the SP 12 major industry stock price indices and 3 individual oil company stock price series. We also examine the extent to which price changes or returns in one market dynamically lead returns in the others and whether volatility spillover effects exist across these markets. Using VAR model estimates for various time series of returns we find that petroleum industry stock index and our three oil company stocks are the only series where we can reject the null hypothesis that oil futures do not lead Treasury Bill rates and stock returns, while we can reject the hypothesis that oil futures lag these other two series. Finally, the return volatility evidence for oil futures leading individual oil company stocks is much weaker than is the evidence for returns themselves.
851 citations
References
More filters
TL;DR: In this paper, the authors use an intertemporal general equilibrium asset pricing model to study the term structure of interest rates and find that anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices.
Abstract: This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the term structure embodies the market's anticipations of future events. An explanation of the term structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the term structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis. These place predominant emphasis on the expected values of future spot rates or holdingperiod returns. In its simplest form, the expectations hypothesis postulates that bonds are priced so that the implied forward rates are equal to the expected spot rates. Generally, this approach is characterized by the following propositions: (a) the return on holding a long-term bond to maturity is equal to the expected return on repeated investment in a series of the short-term bonds, or (b) the expected rate of return over the next holding period is the same for bonds of all maturities. The liquidity preference hypothesis, advanced by Hicks [16], concurs with the importance of expected future spot rates, but places more weight on the effects of the risk preferences of market participants. It asserts that risk aversion will cause forward rates to be systematically greater than expected spot rates, usually
7,014 citations
TL;DR: In this article, it is shown that continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing, managing, and abandoning them.
Abstract: Notwithstanding impressive advances in the theory of finance over the past 2 decades, practical procedures for capital budgeting have evolved only slowly. The standard technique, which has remained unchanged in essentials since it was originally proposed (see Dean 1951; Bierman and Smidt 1960), derives from a simple adaptation of the Fisher (1907) model of valuation under certainty: under this technique, expected cash flows from an investment project are discounted at a rate deemed appropriate to their risk, and the resulting present value is compared with the cost of the project. This standard textbook technique reflects modern theoretical developments only insofar as estimates of the discount rate may be obtained from crude application of single period asset pricing theory (but see Brennan 1973; Bogue and Roll 1974; Turnbull 1977; Constantinides 1978). The inadequacy of this approach to capital budgeting is widely acknowledged, although not widely discussed. Its obvious deficiency is its The evaluation of mining and other natural resource projects is made particularly difficult by the high degree of uncertainty attaching to output prices. It is shown that the techniques of continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing, managing, and abandoning them. The approach may be adapted to a wide variety of contexts outside the natural resource sector where uncertainty about future project revenues is a paramount concern.
2,364 citations
TL;DR: In this article, the authors examine the effects of speculation on economic stability and show that speculative purchases and sales do not necessarily fall into this category, since the main motivation behind such actions is the expectation of a change in the relevant prices relatively to the ruling price and not a gain accruing through their use, or any transformation effected in them or their transfer between different markets.
Abstract: The purpose of the following paper is to examine, in the light of recent doctrines, the effects of speculation on economic stability. Speculation, for the purposes of this paper, may be defined as the purchase (or sale) of goods with a view to re-sale (re-purchase) at a later date, where the motive behind such action is the expectation of a change in the relevant prices relatively to the ruling price and not a gain accruing through their use, or any kind of transformation effected in them or their transfer between different markets. Thus, while merchants and other dealers do make purchases and sales which might be termed ‘speculative’, their ordinary transactions do not fall within this category. What distinguishes speculative purchases and sales from other kinds of purchases and sales is the expectation of an impending change in the ruling market price as the sole motive of action. Hence ‘speculative stocks’ of anything may be defined as the difference between the amount actually held and the amount that would be held if, other things being the same, the price of that thing were expected to remain unchanged; and they can be either positive or negative.1
1,170 citations
"Stochastic Convenience Yield and th..." refers background in this paper
..." See, in particular, Kaldor (1939), Working (1948), Brennan (1986), and Fama and French (1988)....
[...]
Posted Content•
01 Jan 2015
TL;DR: The authors examined two models of commodity futures prices and found evidence of variation in the basis in response to both interest rates and seasonals in convenience yields, and showed evidence of forecast power for 10 of 21 commodities and time-varying expected premiums for five commodities.
Abstract: We examine two models of commodity futures prices. The theory of storage explains the difference between contemporaneous futures and spot prices (the basis) in terms of interest changes, warehousing costs, and convenience yields. We find evidence of variation in the basis in response to both interest rates and seasonals in convenience yields. The second model splits a futures price into an expected premium and a forecast of the maturity spot price. We find evidence of forecast power for 10 of 21 commodities and time-varying expected premiums for five commodities.
937 citations
TL;DR: In this article, the authors examined the pricing of European call options on stocks that have vari? ance rates that change randomly, and they found that one must use the stock and two options to form a riskless hedge.
Abstract: In this paper, we examine the pricing of European call options on stocks that have vari? ance rates that change randomly. We study continuous time diffusion processes for the stock return and the standard deviation parameter, and we find that one must use the stock and two options to form a riskless hedge. The riskless hedge does not lead to a unique option pricing function because the random standard deviation is not a traded security. One must appeal to an equilibrium asset pricing model to derive a unique option pricing function. In general, the option price depends on the risk premium associated with the random standard deviation. We find that the problem can be simplified by assuming that volatility risk can be diversified away and that changes in volatility are uncorrelated with the stock return. The resulting solution is an integral ofthe Black-Scholes formula and the distribution function for the variance of the stock price. We show that accurate option prices can be computed via Monte Carlo simulations and we apply the model to a set of actual prices.
908 citations