THE PRICING OF FUTURES CONTRACTS AND THE ARBITRAGE PRICING THEORY

When interest rates are stochastic, the cash flows of futures and forward contracts differ because of the marking-to-market requirement of futures contracts. The price effect of this difference is examined here by applying the risk and return model of the arbitrage pricing theory. The resulting futures pricing equation is preference free, and is obtainable using other no-arbitrage approaches. The pricing equation suggests that the price difference is due to the covariance of spot asset returns and interest rates. An empirical study is conducted on the Major Market Index futures from October 1, 1984 to September 27, 1985. Results indicate that the covariance, extracted by the Kalman filter according to the pricing equation, is significant in the pricing of futures contracts.     

A PRICING ANOMALY IN TREASURY BILL FUTURES

This research applies an entirely new approach to examining the efficiency of futures markets for Treasury bills and avoids many shortcomings of previous studies that rely on comparing yields on spot versus futures market positions. Efficiency is examined by comparing the consistency of yields within the futures market itself since, at one time, the International Monetary Market (IMM) traded futures contracts for both three-month and one-year bills. The results indicate a remarkably large average annual yield differential of 32 basis points when the yields on the one-year contract are compared to the appropriate corresponding strip of three-month contracts. Possible explanations such as low volume, market thinness, transaction costs, strategy interdependence, serial correlation among differences, and daily resettlement (the Cox, Ingersoll, and Ross effect) are unsuccessful in explaining this pricing anomaly.     

ESTIMATING THE VALUE OF DELIVERY OPTIONS IN FUTURES CONTRACTS

We analyze the effect various delivery options embedded in commodity futures contracts have on the futures price. The two embedded options considered are the timing and location options. We show that early delivery is always optimal when only a timing option is present, but not so when joint options are present. The estimates of the combined options are much smaller than the comparable estimates for the timing option alone. The average value of the joint option is about 5% of the average basis on the first day of the maturity month. This suggests that joint options can increase deliverable supplies while potentially having only a small effect on basis behavior.     

PRICING CURRENCY FUTURES OPTIONS WITH LOGNORMALLY DISTRIBUTED JUMPS

We find that a mixed diffusion-jump process fits most daily currency futures price series better than a mixture of normal densities and, especially, an asymmetric stable Paretian model. We also find that Merton's (1976) mixed diffusion-jump option pricing model outperforms Black's (1 976) model for valuing currency futures options. Our results suggest that researchers should begin to consider the possibility of jump processes as time-independent models of other futures price series.     

SELECTIVE HEDGING OF BANK ASSETS WITH TREASURY BILL FUTURES CONTRACTS

The recent volatility of interest rates, the associated profit pressures imposed on banks, and the surge in the development of new contracts have stimulated a desire to understand and apply financial futures hedging to banking operations. This paper models interest rate futures contracts in a theory of bank behavior to illustrate the hedging of bank loans as well as government securities. The model predicts the hedge will be greater (1) the greater the expected rise in interest rates and (2) the greater the effect of disintermediation on bank deposits. A simulation of the financial futures trading strategy is reported for banks of various asset sizes using data from the Eleventh Federal Reserve District. Depending on bank risk aversion and interest rate expectations, hedging the bank's total interest rate exposure with T-bill futures reduces the variability of unhedged profits by 80 percent.     

A MULTIFACTOR MODEL OF THE QUALITY OPTION IN TREASURY FUTURES CONTRACTS

The values of quality options in Treasury futures contracts are set relative to the prices of all coupon bonds in their respective deliverable sets. As a result, any model used to value the quality option should set its price relative to the set of observed bond prices. This requirement rules out the use of most simple equilibrium models that represent all bond prices in terms of a finite number of state variables. We use the two-factor Heath-Jarrow-Morton model, which permits claims to be priced relative to observable bond prices, to investigate the potential value of the quality option in Treasury bond and note futures. We show that the quality option has significantly more value in a two-factor interest rate economy than in a single-factor economy, and that ignoring it could lead to significant mispricing.     

CHANGING VOLATILITY AND THE PRICING OF OPTIONS ON STOCK INDEX FUTURES

This paper presents empirical results regarding the suitability of the Black model for the pricing of options on stock index futures. Whaley's technique is used to present empirical evidence regarding the pricing biases of the model. Information provided by the implied volatilities suggests that model refinements should address the changing volatility issue.     

OPTION PRICING AND THE ARBITRAGE PRICING THEORY

This paper applies the arbitrage pricing theory to option pricing. Under certain distribution assumptions or the assumption that there is only one common factor, the underlying asset of an option is the sole risky factor that explains its expected return. Based upon this relationship, a new and simple option-pricing formula is derived, and some important existing option-pricing formulae are reproduced. Empirical results show that the new formula performs as well as the Black-Scholes formula.     

FINANCIAL FUTURES AND IMMUNIZATION

This paper investigates the ability of any portfolio that contains both bonds and financial futures contracts to immunize a lump sum liability having the same initial duration and value as the portfolio itself. An analysis of second order conditions shows that immunization against a local change in interest rates is possible only if the number of futures contracts lies within a critical interval; the endpoints depend on cash flow characteristics of the specific bonds and contract being combined. Immunization against any large change in rates is impossible if the portfolio contains any long position in futures but is achieved by some portfolios that contain short positions in futures.