Analytical bounds for Treasury bond futures prices

The pricing of delivery options, particularly timing options, in Treasury bond futures is prohibitively expensive. Recursive use of the lattice model is unavoidable for valuing such options, as Boyle in J Finance 14(1):101?C113, (1989) demonstrates. As a result, the main purpose of this study is to derive upper bounds and lower bounds for Treasury bond futures prices. This study first shows that the popular preference-free, closed form cost of carry model is an upper bound for the Treasury bond futures price. Then, the next step is to derive analytical lower bounds for the futures price under one and two-factor Cox-Ingersoll-Ross models of the term structure. The bound under the two-factor Cox-Ingersoll-Ross model is then tested empirically using weekly futures prices from January 1987 to December 2000.     

中国利率市场的价格发现——对国债现货、期货以及利率互换市场的研究

本文采用信息份额模型和基于向量自回归(VAR)模型的格兰杰因果检验,研究了国债现货、国债期货和利率互换三个市场之间的价格发现机制。信息份额模型表明,从整体来看利率互换相对于国债期货和国债现货都具有信息优势,而国债期货相对于国债现货具有信息优势。另外,国债期货的价格发现能力相对于另外两个市场都在随时间增强。格兰杰因果检验结果显示,利率互换在价格发现中单向引领国债期货以及国债现货,国债期货单向引领国债现货。所有结果一致表明, 利率互换和国债期货这两种利率衍生产品在引导中国利率市场价格发现中发挥了重要作用。     

Valuation and Optimal Exercise of the Wild Card Option in the Treasury Bond Futures Market

The Chicago Board of Trade Treasury Bond Futures Contract allows the short position several delivery options as to when and with which bond the contract will be settled. The timing option allows the short position to choose any business day in the delivery month to make delivery. In addition, the contract settlement price is locked in at 2:00 p .m . when the futures market closes, despite the facts that the short position need not declare an intent to settle the contract until 8:00 p .m . and that trading in Treasury bonds can occur all day in dealer markets. If bond prices change significantly between 2:00 and 8:00 p .m ., the short has the option of settling the contract at a favorable 2:00 p .m . price. This phenomenon, which recurs on every trading day of the delivery month, creates a sequence of 6-hour put options for the short position which has been dubbed the “wild card option.” This paper presents a valuation model for the wild card option and computes estimates of the value of that option, as well as rules for its optimal exercise.     

A continuous time equilibrium model of forward prices and futures prices in a multigood economy

This paper is a theoretical investigation of equilibrium forward and futures prices. We construct a rational expectations model in continuous time of a multigood, identical consumer economy with constant stochastic returns to scale production. Using this model we find three main results. First, we find formulas for equilibrium forward, futures, discount bond, commodity bond and commodity option prices. Second, we show that a futures price is actually a forward price for the delivery of a random number of units of a good; the random number is the return earned from continuous reinvestment in instantaneously riskless bonds until maturity of the futures contract. Third, we find and interpret conditions under which normal backwardation or contango is found in forward or futures prices; these conditions reflect the usefulness of forward and futures contracts as consumption hedges.     

The Quality Delivery Option in Treasury Bond Futures Contracts

This paper uses three methods to estimate quality option values for CBOT Treasury bond futures contracts. It presents evidence regarding: (1) payoffs from exercising this option at delivery, (2) estimates from a T-bond futures pricing model that incorporates this option, and (3) estimates obtained from an exchange option pricing formula. The results indicate that this option is worth considerably less than reported by Kane and Marcus (1986a) . For example, payoffs obtained by switching from the bond cheapest to deliver three months prior to delivery to the one cheapest at time of delivery average less than 0.30 percentage points of par.     

Term structure estimation and pricing of callable Treasury bonds

This article describes a methodology of term structure estimation incorporating callable Treasury bonds using a bond-option valuation model. This article also examines whether some simple approximation of the option value suffice for providing a useful estimation procedure. The authors find that the errors in estimating the option value can generate significant errors for estimating the discount function. A call provision on a Treasury bond is not negligible at least our framework. This procedure is consistent with two aspects of the Treasury market. First, it provides the discount function that best determines the prices of observed Treasury securities, and second, it obtains a discount function that explains callable Treasuries.     

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.     

Hedging Corporate Bonds

We examine Treasury bond and stock index futures, the swap curve and two types of hypothetical corporate bond assets as alternative hedging instruments for portfolios of corporate bonds. Conducting ex post and ex ante tests we find evidence that credit quality and maturity are important sources of basis risk when hedging corporate bonds whose credit rating are below triple A. We conclude that a new corporate hedging instrument may be useful for those wishing to hedge corporate bond portfolios provided that transaction costs are not too high relative to existing futures contracts.     

Order flow and volatility: An empirical investigation

We study the relationship between order flow and volatility. To this end we develop a comprehensive framework that simultaneously controls for the effects of macro announcements and order flow on prices and the effect of macro announcements on volatility. Using high-frequency 30-year U.S. Treasury bond futures data, we find a statistically and economically significant relationship between the absolute value of order flow and volatility. Moreover, this relationship is robust, inter alia, to a number of factors including the introduction of liquidity effects, use of data measured over a different frequency, and market conditions.     

引入国债期货合约能否发挥现货市场稳定效应?——基于中国金融周期的研究视角

我国国债期货市场能否发挥稳定现货市场功能,金融周期风险是否会改变国债期货市场对现货市场波动的影响,是投资者实施风险管理和监管部门构建市场稳定机制的重要依据。本文通过信息传递机制和交易者行为两个维度探析国债期货市场发挥稳定功能的微观机理,分析金融周期风险对衍生工具稳定功能的影响,解析引入国债期货合约能否缓解金融周期波动对国债市场冲击,同时关注我国国债期货交易机制改进与现券波动关系。研究发现:(1)我国国债期货市场已实现抑制现货市场波动的功能,金融周期风险会引发现货价格波动,国债期货市场能够降低金融周期的波动冲击;(2)改善现货市场深度和套保交易是国债期货市场发挥稳定功能的微观路径,国债期货市场增进国债预期交易量流动性、减弱非预期交易量干扰,金融周期低波动区间套保交易稳定作用受到抑制;(3)国债期货投机交易和波动溢出效应助长现货市场波动,正负期现基差对国债波动影响具有非对称特征。     

The Quality Option and Timing Option in Futures Contracts

Often futures contracts contain quality options whereby the short position has the choice of delivering one of an acceptable set of assets. We explore the implications of the quality option on the futures price. We develop a method for pricing the quality option for the general case of n deliverable assets and provide numerical illustrations of its significance. Even when the asset prices are very highly correlated, this option can have nontrivial value, especially when there is a large number of deliverable assets. We analyze the impact of the timing option and its interaction with the quality option. A procedure is developed for valuing the timing option in the presence of the quality option, and some numerical estimates are obtained.     

Macroeconomic news and treasury futures return volatility: Do treasury auctions matter?

Various macroeconomic announcements are known to influence asset price volatility. In addition to non-farm payrolls, we highlight the importance of Treasury auctions – a news event that has grown in importance due to ongoing Federal deficits. The occurrence of an auction, which increases supply in the underlying cash market, pushes futures prices lower and volatility higher. Conversely, a higher bid-to-cover ratio, indicates greater demand for Treasury securities, increases Treasury futures prices and lowers volatility. The response is consistent with market participants using futures to manage inventory risk. The results are consistent across a set of volatility estimates, and in an alternate conditional volatility framework.     

Pricing interest rate options in a two-factor Cox-Ingersoll-Ross model of the term structure

Solutions are presented for prices on interest rate optionsin a two-factor version of the Cox-Ingersoll-Ross model of theterm structure. Specific solutions are developed for caps onfloating interest rates and for European options on discountbonds, coupon bonds, coupon bond futures, and Euro-dollar futures.The solutions for the options are expressed as multivariateintegrals, and we show how to reduce the calculations to univariatenumerical integrations, which can be calculated very quickly.The two-factor model provides more flexibility in fitting observedterm structures, and the fixed parameters of the model can beset to capture tie variability of the term structure over time.     

Modelling the Implied Volatility of Options on Long Gilt Futures

This paper investigates the properties of implied volatility series calculated from options on Treasury bond futures, traded on LIFFE. We demonstrate that the use of near-maturity at the money options to calculate implied volatilities causes less mis-pricing and is therefore superior to, a weighted average measure encompassing all relevant options. We demonstrate that, whilst a set of macroeconomic variables has some predictive power for implied volatilities, we are not able to earn excess returns by trading on the basis of these predictions once we allow for typical investor transactions costs.     

Alternative models for hedging yield curve risk: An empirical comparison

We test alternative models of yield curve risk by hedging US Treasury bond portfolios through note/bond futures. We show that traditional implementations of models based on principal component analysis, duration vectors and key rate duration lead to high exposure to model errors and to sizable transaction costs, thus lowering the hedging quality. Also, this quality randomly varies from one model and hedging problem to the other. We show that accounting for the variance of modeling errors substantially reduces both hedging errors and transaction costs for all considered models. Additionally, it leads to much more stable weights in the hedging portfolios and – as a result – to more homogeneous hedging quality. On this basis, error-adjusted principal component analysis is found to systematically and significantly outperform alternative models.     

On the valuation of an option to exchange one interest rate for another

This paper studies the problem of pricing a European option on the difference of two interest rates, which is analogous to an option to exchange one asset for another, studied in Margrabe (1978). It is first shown that such option may be valued as exchanging two interest rates implied in relevant futures prices through an extended Black (1976) model, and then by a two-factor Heath-Jarrow-Morton (HJM) model, which shows that introduction of imperfect interest rates movements is essential for pricing such options, for which a one-factor model such as Ho and Lee (1986) should not be applied.     

Price adjustment to news with uncertain precision

We analyze how markets adjust to new information when the reliability of news is uncertain and has to be estimated itself. We propose a Bayesian learning model where market participants receive fundamental information along with noisy estimates of news’ precision. It is shown that the efficiency of a precision estimate drives the slope and the shape of price response functions to news. Increasing estimation errors induce stronger nonlinearities in price responses. Analyzing high-frequency reactions of Treasury bond futures prices to employment releases, we find strong empirical support for the model’s predictions and show that the consideration of precision uncertainty is statistically and economically important.     

Spot and derivative pricing in the EEX power market

Using spot and futures price data from the German EEX Power market, we test the adequacy of various one-factor and two-factor models for electricity spot prices. The models are compared along two different dimensions: (1) We assess their ability to explain the major data characteristics and (2) the forecasting accuracy for expected future spot prices is analyzed. We find that the regime-switching models clearly outperform its competitors in almost all respects. The best results are obtained using a two-regime model with a Gaussian distribution in the spike regime. Furthermore, for short and medium-term periods our results underpin the frequently stated hypothesis that electricity futures quotes are consistently greater than the expected future spot, a situation which is denoted as contango.     

Financial Innovation and the Role of Derivative Securities: An Empirical Analysis of the Treasury STRIPS Program

The role that financial innovation plays in financial markets is very controversial. To provide insight into this role, we examine how market participants use the highly successful Treasury STRIPS program. We find that investors use the option to create Treasury-derivative STRIPS primarily to make markets more complete and take advantage of tax and accounting asymmetries. Although liquidity-related factors help explain differences in the prices of Treasury bonds and STRIPS, we find little evidence that the option to strip and reconstitute securities is used for speculative or arbitrage-related purposes.     

International tax arbitrage,currency options and put-call parity conditions

Using a finite-horizon general equilibrium model with uncertainty and money, we characterize situations where tax arbitrage opportunities may arise for international portfolio investors in an economy with heterogeneous capital income taxation where foreign currency exposure can be hedged using forward contracts and a set of currency options. We obtain tax-modified option prices similar to the no-tax ones, but augmented by tax-induced “risk-premium” terms; tax-modified put-call parity conditions are derived that revert to their standard (no-tax) format if the respective marginal agents in the bond and option markets are in identical tax brackets.