PRICING CURRENCY OPTIONS UNDER STOCHASTIC INTEREST RATES AND JUMP‐DIFFUSION PROCESSES

We investigate the effects of stochastic interest rates and jumps in the spot exchange rate on the pricing of currency futures, forwards, and futures options. The proposed model extends Bates's model by allowing both the domestic and foreign interest rates to move around randomly, in a generalized Vasicek term‐structure framework. Numerical examples show that the model prices of European currency futures options are similar to those given by Bates's and Black's models in the absence of jumps and when the volatilities of the domestic and foreign interest rates and futures price are negligible. Changes in these volatilities affect the futures options prices. Bates's and Black's models underprice the European currency futures options in both the presence and the absence of jumps. The mispricing increases with the volatilities of interest rates and futures prices. JEL classification: G13     

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.     

PRICING CRB FUTURES CONTRACTS

This study provides a valuation model to price Commodity Research Bureau Index futures contracts, now traded at the New York Futures Exchange. An empirical analysis suggests that substantial mispricing was exhibited during the early months of trading in an unseasoned Commodity Research Bureau Index futures market.     

Futures Options and the Volatility of Futures Prices

Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at-the-money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.     

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.     

A Comparison of Forward and Futures Prices of an Interest Rate-Sensitive Financial Asset

This paper focuses on contractual distinctions as an explanation for the price divergence between futures and forward contracts. Specifically, it investigates the effect of marking-to-market on the observed price differences using the pricing model described in Cox, Ingersoll, and Ross (CIR) (1981, Journal of Financial Economics 9, 321–346). Using previously unavailable data, this paper employs Eurodollars, an interest rate-sensitive financial asset, to test the CIR model. Unlike prior empirical studies, test results support both the weak prediction concerning the sign of the average price difference and the stronger prediction that specific covariances explain the variation in the price differences.     

Can the choice of interpolation method explain the difference between swap prices and futures prices?

The standard model linking the swap rate to the rates in a contemporaneous strip of futures interest rate contracts typically produces biased estimates of the swap rate. Institutional differences usually require some form of interpolation to be employed and may in principle explain this empirical result. Using Australian data, we find evidence consistent with this explanation and show that model performance is greatly improved if an alternative interpolation method is used. In doing so, we also provide the first published Australian evidence on the accuracy of the futures‐based approach to pricing interest rate swaps.     

The quality option implicit in futures contracts

The quality option implicit in futures contracts allows the short position to satisfy the contract by delivering one of a variety of specified assets. If, at the time the contract is purchased, knowledge of which of the allowed assets will be cheapest at maturity is uncertain, then the quality option will have value. The greater the value of this option, the lower will be the futures price. This paper presents, and tests, a futures pricing model that incorporates the quality option aspect of commodity futures contracts. Our research shows that the quality option has a significant impact on futures prices.     

An analysis of the true notional bond system applied to the CBOT T-bond futures

The conversion factor system (CFS) is used in the determination of the invoice price of the Chicago Board of Trade Treasury-bond futures. As an alternative to the CFS, Oviedo [Oviedo, R.A., 2006. Improving the design of Treasury-Bond futures contracts. The Journal of Business 79, 1293–1315] proposed the True Notional Bond System (TNBS), and showed that it outperforms the CFS when interest rates are deterministic. The main purpose of this paper is to compare the effectiveness of the two systems in a stochastic environment. In order to do so, we price the CBOT T-bond futures as well as all its embedded delivery options under both the CFS and the TNBS. Our pricing procedure is an adaptation of the Dynamic Programming algorithm described in Ben-Abdallah et al. [Ben-Abdallah, R., Ben-Ameur, H., Breton, M., 2007. Pricing CBOT Treasury Bond futures. Les Cahiers du GERAD G-2006-77]. Numerical illustrations show that, in a stochastic framework, TNBS does not always outperform the CFS. However, as the long-term mean moves away from the level of the notional rate, the TNBS performs increasingly better than the CFS.     

The Valuation of Options on Futures Contracts

Rational restrictions are derived for the values of American options on futures contracts. For these options, the optimal policy, in general, involves premature exercise. A model is developed for valuing options on futures contracts in a constant interest rate setting. Despite the fact that premature exercise may be optimal, the value of this American feature appears to be small and a European formula due to Black serves as a useful approximation. Finally, a model is developed to value these options in a world with stochastic interest rates. It is shown that the pricing errors caused by ignoring the location of the interest rate (relative to its long-run mean) range from ?5% to 7%, when the current rate is ±200 basis points from its long-run value. The role of interest rate expectations is, therefore, crucial to the valuation. Optimal exercise policies are found from numerical methods for both models.     

THE HEDGING EFFECTIVENESS OF FOREIGN CURRENCY FUTURES

This study provides an initial analysis of the hedging potential of the foreign currency futures markets. Numerous studies exist on the pricing efficiency and hedging effectiveness of the foreign currency forward markets, but little research exists on the foreign currency futures market. An adequate price history has only recently become available to carry out such an investigation. Minimum risk hedges and hedging effectiveness measures are presented for five currencies: the British pound, German mark, Canadian dollar, Japanese yen and Swiss franc. Analysis indicates the relative desirability of positions in futures contracts to minimize the risk of spot currency exposure. Results also show hedging effectiveness increases with the investment horizon.     

Pricing Efficiency and Arbitrage in the Bitcoin Spot and Futures Markets

This study examines the pricing efficiency for the leading cryptocurrency, Bitcoin using spot prices and all CBOE and CME futures contracts traded from January 2018 to March 2019. We find that the futures basis provide some predictive power for future changes in the spot price and in the risk premium. However, the basis of Bitcoin is a biased predictor of the future spot price changes. Cointegration tests also demonstrate that futures prices are biased predictors of spot prices. Deviations from no-arbitrage between spot and futures markets are persistent and widen significantly with Bitcoin thefts (hacks, frauds) as well as alternative cryptocurrency issuances.     

Tests of alternate models for the pricing of Korean Treasury bond futures contracts

It is known that KTB futures contracts are significantly underpriced when the model price is calculated using the ad hoc cost-of-carry model employed in industry. This paper examines whether this underpricing phenomenon is caused by using the wrong model to price the futures contracts. This paper documents that the difference between the model price and the market price of KTB futures decreases substantially if the correct term–structure-based model is used to estimate the model price of KTB futures. In addition, even though the underpricing phenomenon can be exploited to generate some trading profits, the profits cannot be regarded as arbitrage profits. Thus, we believe that the underpricing phenomenon is illusory, and that much of it can be attributed to the wrong model being used in the industry.     

Do economic statistics contain information to predict stock indexes futures prices and returns? Evidence from Asian equity futures markets

This research examines the impact of local and international market factors on the pricing of stock indexes futures in East Asian countries. The purpose of this paper is to present a study of the significant factors that determine the major stock indexes futures’ prices of Hong Kong, Malaysia, Singapore, South Korea and Taiwan. This study first investigates the relationships between Hang Seng Index Futures, KLCI Futures, SiMSCI Futures, KOSPI Futures, Taiwan Exchange Index Futures and local interest rates, dividend yields, local exchange rates, overnight S&P500 index and a newly constructed index, Asian Tigers Malaysia Index (ATMI). 11 years historical data of stock indexes futures and the economic statistics are studied; 10 years in-sample data are used for testing and developing the pricing models, and 1 year out-of-sample data is used for the purpose of verifying the predicted values of the stock indexes futures. Using simple linear regressions, local interest rates, dividend yields, exchange rates, overnight S&P500 and ATMI are found to have significant impact on these futures contracts. In this research, the next period close is predicted using simple linear regression and non-linear artificial neural network (ANN). An examination of the prediction results using nonlinear autoregressive ANN with exogenous inputs (NARX) shows significant abnormal returns above the passive threshold buy and hold market returns and also above the profits of simple linear regression (SLR). The empirical evidence of this research suggests that economic statistics contain information which can be extracted using a hybrid SLR and NARX trading model to predict futures prices with some degree of confidence for a year forward. This justifies further research and development of pricing models using fundamentally significant economic determinants to predict futures prices.

     

Stochastic Convenience Yield and the Pricing of Oil Contingent Claims

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.     

Optimal portfolios in commodity futures markets

We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios of futures contracts. In the portfolio optimization problem, the agent invests in futures contracts and a risk-free asset, and her objective is to maximize the utility from final wealth. In order to capture self-consistent futures price dynamics, we study a class of futures price curve models which admit a finite-dimensional realization. More precisely, we establish conditions under which the futures price dynamics can be realized in finite dimensions. Using the finite-dimensional realization, we derive a finite-dimensional form of the portfolio optimization problem and study its solution. We also give an economic interpretation of the coordinate process driving the finite-dimensional realization.     

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.     

A Pricing Framework for Real Estate Derivatives

New methods are developed here for pricing the main real estate derivatives — futures and forward contracts, total return swaps, and options. Accounting for the incompleteness of this market, a suitable modelling framework is outlined that can produce exact formulae, assuming that the market price of risk is known. This framework can accommodate econometric properties of real estate indices such as predictability due to autocorrelations. The term structure of the market price of risk is calibrated from futures market prices on the Investment Property Databank index. The evolution of the market price of risk associated with all five futures curves during 2009 is discussed.     

LIQUIDITY AND PRICE VARIABILITY IN FUTURES MARKETS

This paper tests the hypothesis that market liquidity affects the price variability of futures contracts. The analyses used take into account the maturity effect and various sources of nonstationarity. Empirical testing involved eleven commodities in various markets. The evidence strongly suggests that futures contracts in distant and thinly traded months exhibit different price variability than contracts in near to maturity and liquid traded months, and that the behavior is commodity dependent. These findings could help investors better evaluate risks and provide a better basis for hedging strategies. Also, monthly averages of open interest can be used interchangeably with volume to measure liquidity in determining which pattern applies to a given commodity.     

Optimal Hedging in Futures Markets with Multiple Delivery Specifications

Nearly all futures contracts allow delivery of any of several qualities of the underlying asset. Consequently, the price of the futures contract is associated more with the price of the expected cheapest deliverable variety than with the price of the par-delivery variety. The delivery specifications introduce a delivery risk for every hedger in the market. We derive the optimal hedging strategies in these markets. Their hedging effectiveness is evaluated for wheat futures contracts in Chicago. Hedging optimally would have significantly reduced the variance of the rates of return on hedges while yielding similar mean returns.