ContentsA Strategic Analysis of Corners and SqueezesDavid J. Cooper and R. Glen Donaldson
Valuation of Commodity Futures and Options under
Stochastic Convenience Yields, Interest Rates,
and Jump Diffusions in the Spot
Permanent, Temporary, and Non-Fundamental Components of Stock Prices
Pricing of Options on Commodity Futures with
Stochastic Term Structures of Convenience Yields and Interest Rates
Pricing Term Structure Risk in Futures Markets
Loan Commitments and the Debt Overhang Problem |
AbstractsA Strategic Analysis of Corners and Squeezes We develop a dynamic game-theoretic model of a futures market in which prices can be manipulated by corner and squeeze. We investigate equilibrium trading strategies and the price dynamics these strategies produce. Price paths produced by our model can mimic observed prices for potentially cornerable commodities and explain the volatility of certain prices even when no manipulations occur. Our model also generates occasional apparent price bubbles and accounts for the existence of normal backwardation in futures markets even when players are risk neutral.
Valuation of Commodity Futures and Options under
Stochastic Convenience Yields, Interest Rates,
and Jump Diffusions in the Spot This paper investigates the effects of stochastic convenience yields, stochastic interest rates, and jumps in the spot price on the pricing of commodity futures, forwards, and futures options. Numerical examples show that one-factor prices differ materially from the stochastic convenience yield two-factor prices when convenience yield is considerably above its long-term average. The extension to a three-factor model with stochastic interest rates leads to a different futures price but the forward price is unchanged. The extension of the three-factor model to include jumps in the spot price process does not affect forward or futures prices but it can have an impact on options prices. The model is applied to price the present value of future cash flows from a real asset.
Permanent, Temporary, and Non-Fundamental Components of Stock Prices This paper identifies various components of stock prices and examines the response of stock prices to different types of shocks: permanent and temporary changes in earnings and dividends, changes in discount factors, and non-fundamental factors. The analysis is conducted in a log-linear structural VAR framework. I find that about half of the yearly variation in prices is not related to either earnings or dividend changes. Time-varying interest rates do not help explain the remaining price movements. However, time-varying excess stock returns (i.e., risk premiums) account for much of the remaining variation in stock prices, in particular, in the postwar period. As a result, the deviation of stock prices from these fundamentals reduces to about 10% of stock price movements and tends to persist for a while before it declines eventually. This finding seems more compatible with a fad rather than a bubble interpretation.
Pricing of Options on Commodity Futures with
Stochastic Term Structures of Convenience Yields and Interest Rates We develop a model to value options on commodity futures in the presence of stochastic interest rates as well as stochastic convenience yields. In the development of the model, we distinguish between forward and future convenience yields, a distinction that has not been recognized in the literature. Assuming normality of continuously compounded forward interest rates and convenience yields and log-normality of the spot price of the underlying commodity, we obtain closed-form solutions generalizing the Black-Scholes/Merton's formulas. We provide numerical examples with realistic parameter values showing that both the effect of introducing stochastic convenience yields into the model and the effect of having a short time lag between the maturity of a European call option and the underlying futures contract have significant impact on the option prices.
Pricing Term Structure Risk in Futures Markets One-period expected returns on futures contracts with different maturities differ because of risk premia in the spreads between futures and spot prices. We analyze the expected returns for futures contracts with different maturities using the information that is present in the current term structure of futures prices. A simple affine one-factor model that implies a constant covariance between the pricing kernel and the cost-of-carry cannot be rejected for heating oil and German Mark futures contracts. For gold and soybean futures, the risk premia depend on the slope of the current term structure of futures prices, while for live cattle futures, the evidence is mixed.
Loan Commitments and the Debt Overhang Problem The debt overhang problem is shown to arise in the context of an entrepreneurial project that requires a sequence of investments financed by an outside lender. The entrepreneur, not internalizing losses accruing to the lender which financed the initial investments, may inefficiently cancel the project and instead pursue an outside opportunity. It is shown that loan commitments (contracts that allow the entrepreneur to borrow a variable amount at a set interest rate in return for a fixed fee) are the optimal financial contracts in this setting, strictly dominating standard debt. The existence of the fixed fee allows loan commitments to set a relatively low interest rate, improving the entrepreneur's incentives to continue the project. The paper specifies the optimal contract fully, derives robust comparative statics properties (using an extension of Milgrom and Roberts (1994)), and extends the results to more realistic settings (e.g., allowing the market risk-free rate to be stochastic).
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