Using futures contracts for corporate hedging: The problem of expiry and a possible solution

Companies using futures contracts for hedging purposes need to roll over their contracts if the maturity of their exposure exceeds that of the futures contracts. This entails basis risk that can reduce significantly the effectiveness of the hedge. In this paper an alternative form of futures contract is proposed. the contract never expires and can be used for long-term hedging without the need for rolling-over into a new contract. the contract is shown to be equivalent to a portfolio of conventional futures contracts of differing maturities. Its price is determined by arbitrage against the underlying asset.     

Strategic commodity allocation

This article extends the study of the financialization of commodities (Rouwenhorst and Tang [Annu. Rev. Financ. Econ., 2012, 4, 447–467]) by considering an investment in the term structure of commodity futures prices. Specifically, we analyse the benefits of adding a distant commodity futures contract and/or a spot commodity (near month futures contract) to a portfolio of bonds and stocks in a setting similar to Brennan and Schwartz [The use of treasury bill futures in strategic asset allocation programs. In Worldwide Asset and Liability Modeling, edited by W.T. Ziemba and J.M. Mulvey, pp. 205–230, 1998 (Cambridge University Press: Cambridge)]. Our analysis employs an empirical study that covers the post financial crisis period. We show that the spot commodity considerably improves the value of the portfolio. However, an investment in the whole term structure of futures contracts is optimally achieved through high opposite positions in the spot commodity and distant futures contracts. We find that these extreme calendar spreads can result in an inappropriate investment.     

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.     

Optimal dynamic hedging in incomplete futures markets

This article derives optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of either a CARA or a logarithmic utility function. Existing futures contracts are not numerous enough to complete the market. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding, and the optimal hedging demands are not identical to those that would be derived if the constraint were ignored. Fictitiously completing the market, we can characterize the optimal hedging demands for futures contracts. Closed-form solutions exist in the logarithmic case but not in the CARA case, since then a put (insurance) written on his wealth is implicitly bought by the investor. Although solutions are formally similar to those that obtain under complete markets, incompleteness leads in fact to second-best optima.     

Currency risk hedging: Futures vs. forward

The objective of this paper is to address the issue of choosing between currency forward and currency futures contracts when hedging against currency risk within a stochastic interest rates environment. We compare between the hedging effectiveness of the two derivative assets both within a narrow sense (i.e., volatility minimization) and within a wide sense (i.e., risk-return trade-off). When judging hedging effectiveness in the narrow sense, forward and futures contracts give identical results even if they do not have identical prices. When judging hedging effectiveness in the wide sense, the choice between the two contracts is determined by the correlation between the domestic and the foreign term structures dynamics.     

A simple approach to interest-rate option pricing

A simple introduction to contingent claim valuation of riskyassets in a discrete time, stochastic interest-rate economyis provided. Taking the term structure of interest rates asexogenous, closed-form solutions are derived for European optionswritten on (i) Treasury bills, (ii) interest-rate forward contracts,(iii) interest-rate futures contracts, (iv) Treasury bonds,(v) interest-rate caps, (vi) stock options, (vii) equity forwardcontracts, (viii) equity futures contracts, (ix) Eurodollarliabilities, and (x) foreign exchange contracts.     

Futures-Style Options on Euro-deposit Futures: Nihil sub Sole Novi?

Euro-deposit futures play a relevant role among the derivative products traded in official markets. As opposed to most futures contracts, the underlying instrument is not represented by a traded asset but by a linear transformation of an interest rate, the Libor. The options written on Euro-deposit futures that are traded at the London International Financial Futures & Options Exchange (LIFFE) are subject to daily marking to market, as the underlying futures; thus, they are called futures-style options or pure futures options. These options are often priced with the Black (1976) formula, whose use entails several shortcomings. A more realistic alternative is represented by the univariate Cox, Ingersoll and Ross (1985) model. The closed-form solutions for the prices of Euro-deposit futures and futures-style options on Euro-deposit futures obtained in the CIR model are two major original contributions presented in this paper. Other original contributions involve the determination of the relation between futures rates and forward rates and the derivation of the equivalent portfolio for the hedging of futures-style options on Euro-deposit futures.     

Constrained dynamic futures portfolios with stochastic basis

Annals of Finance - We study the problem of dynamically trading multiple futures contracts on different underlying assets subject to portfolio constraints. The spreads between futures and spot...     

Trading House Price Risk with Existing Futures Contracts

This paper examines the use of futures contracts to hedge residential real estate price risk. We examine whether existing futures contacts can effectively be used to offset volatility in national house prices. Little evidence of any simple systematic relation between national prices and futures prices is found. Since house prices are not easily replicated with a portfolio of existing futures contracts, a further implication is that the Chicago Mercantile’s introduction of a financial asset whose value reflects house prices will help complete the market. Nevertheless, the success of the CME’s new derivative contracts may be limited in light of state and regional house price correlations.

期货投资组合交易保证金设置研究——基于Copula模型和极值理论的分析

本文以棉花、铜、天然橡胶三个期货合约为研究对象,基于t-Copula模型,利用Monte Carlo模拟法计算在一定权重下由三个品种构成的期货投资组合的VaR和ES值作为投资组合的保证金数值。Kupiec回溯测试结果表明,t-Copula模型结合极值理论计算出的期货投资组合保证金相比其他方法能够在较好覆盖极端风险的同时降低投资成本。     

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.     

The nominal duration of TIPS bonds

This paper studies the price responsiveness (effective duration) of U.S. government issued inflation-indexed bonds, known by the acronym TIPS (Treasury Inflation-Protected Securities), to changes in nominal interest rates, real interest rates, and expected inflation. Using the TIPS pricing formula derived by Laatsch and Klein [Q. Rev. Econ. Finance 43 (2002) 405], we first confirm that TIPS bonds have zero sensitivity to changes solely in expected inflation. By changes solely in expected inflation, we mean that the real rate remains unchanged and the nominal rate changes in accordance with the established Fisher [Publ. Am. Econ. Assoc. 11 (1896)] effect. We show that the first derivative of the TIPS price is zero whenever the real rate is held constant. Thus, the first partial derivative of the TIPS bond pricing formula with respect to expected inflation is zero and the first partial derivative of the TIPS bond price with respect to nominal rates is also zero, given, in each case, that we hold the real rate constant. We then temporarily shift the analysis to zero-coupon TIPS bonds and zero-coupon ordinary Treasury bonds. We prove that the nominal duration of zero-coupon TIPS bonds equals that of zero-coupon ordinary Treasury bonds when the real rate changes but expected inflation is held constant.However, if expected inflation changes and the change in the nominal rate does not yield a constant real rate, zero-coupon TIPS prices will change and they will change by a smaller percentage than will zero-coupon ordinary Treasury bonds. We analyze TIPS responsiveness to changes in nominal rates under such conditions. We derive an approximation to effective duration that demonstrates that the effective durations of various maturity zero-coupon TIPS bonds are approximately linear functions in time to maturity of the effective duration of the one-year zero-coupon TIPS bond, ceteris paribus.Nominal effective duration of TIPS bonds is certainly of interest to fixed income portfolio managers that might have a desire to include such bonds in their portfolio. After all, the greater portion of a typical fixed income portfolio is in traditional, noninflation protected bonds whose major risk exposure is to changes in nominal rates. To properly assess the role of TIPS bonds in the portfolio, portfolio managers need information as to how TIPS bonds respond to the changes in nominal rates that are driving the price behavior of the bulk of the portfolio's assets. Prior to concluding the paper, we demonstrate how portfolio managers can calculate the nominal durations of coupon TIPS bonds using the zero-coupon duration formula we derive.     

Investment Decision Making with Derivative Securities

This paper examines strategies employing stock options, index options, index futures options, and index futures contracts in an effort to establish under what conditions a portfolio manager should diversify into these derivative assets. The results show that futures option call writing and put buying were dominated by third-order stochastic dominance when compared to similar index options. Thus, when covered call writing or protective put buying are being considered, index options appear to be the better choice.     

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.     

Trading activity and price reversals in futures markets

We use the standard contrarian portfolio approach to examine short-horizon return predictability in 24 US futures markets. We find strong evidence of weekly return reversals, similar to the findings from equity market studies. When interacting between past returns and lagged changes in trading activity (volume and/or open interest), we find that the profits to contrarian portfolio strategies are, on average, positively associated with lagged changes in trading volume, but negatively related to lagged changes in open interest. We also show that futures return predictability is more pronounced if interacting between past returns and lagged changes in both volume and open interest. Our results suggest that futures market overreaction exists, and both past prices and trading activity contain useful information about future market movements. These findings have implications for futures market efficiency and are useful for futures market participants, particularly commodity pool operators.     

Forward contracts and futures contracts

This paper provides a detailed discussion of the similarities and differences between forward contracts and futures contracts. Under frictionless markets and continuous trading, simple arbitrage arguments are invoked to value forward contracts, to relate forward prices and spot prices, and to relate forward prices and futures prices. We also argue that forward prices need not equal futures prices unless default free interest rates are deterministic.     

Evidence on the arbitrage efficiency of SPI index futures and options markets

This paper is concerned with arbitrage opportunities in the futures and futures option contracts traded on the Sydney Futures Exchange (SFE) within a put-call-futures-parity (PCFP) framework. Tick-by-tick transaction price data are employed so that the futures contracts, the call futures options and the put futures options can be matched within a one-minute interval. This paper also takes into account the realistic transaction costs that an arbitrager has to incur, including the implicit bid-ask spread. A thorough ex post analysis is first carried out. The results reveal a significant number of violations of the PCFP in the sample. Ex ante tests are then conducted whereby ex post profitable arbitrage strategies, signified by the matched trios of futures, put and call contracts, are executed with lags up to 3 min. The ex ante results are similar to the ex post results. However, further analysis reveals that the exploitability of the identified arbitrage opportunities is very limited due to the small trading volumes of the futures and options contracts. Thus, we conclude that there is no strong evidence against the arbitrage efficiency between the SPI index futures and options markets in Australia.      

Who trades bitcoin futures and why?

Using regulatory data with identifiers, we analyze the traders active in the Bit- coin futures (BTC) contracts traded on the Chicago Mercantile Exchange (CME). We find two primary trader types, those who hold almost exclusively BTC (con- centrated traders) and those who hold BTC to diversify a broader futures portfolio (diversified traders). The prevalence of these two types changes over time. We also study how BTC markets are connected to other futures markets through common holdings of BTC traders. Finally, we analyze the micro BTC contract and find that the trader composition is different than that of the full-size contract.     

Dynamic portfolio choice with deferred annuities

We derive the optimal life-cycle portfolio choice and consumption pattern for households facing uncertain labor income, risky capital market, and mortality risk. In addition to stocks and bonds, the households have access to deferred annuities. Deferred payout life annuities are financial contracts providing life-long income to the annuitant after a specified period of time conditional on survival. We find that deferred annuities play an important role in household portfolios and generate significant welfare gains. Households with high benefits from state pensions, moderate risk aversion and moderate labor income risk purchase deferred annuities from age 40 and gradually increase their portfolio share. At retirement, deferred annuities account for 78% of total financial wealth. Households with low state pensions and high labor income risk purchase more annuities and earlier. Uncertainty with respect to future mortality rates has the same effect, i.e. household hedge against longevity risks using deferred annuities.     

The Effect of Policyholder Transfer Behavior on the Value of Guaranteed Minimum Death Benefits

Abstract

Variable annuity contracts frequently include both guaranteed minimum death benefit (GMDB) options and options to transfer funds between fixed and variable accounts. We model the difference between fixed and variable rates as the primary determinant of policyholder transfer behavior. We find that people tend to transfer their money into variable accounts at about 39% of the rate that would be required to maintain constant percentage rebalancing, but with the opposite sign. If these transfers are not taken into account, the GMDB options on the variable accounts will be overvalued and overhedged. Ignoring this effect can have a substantial impact on the size of the futures portfolio needed to hedge this risk and a nonnegligible impact on the earnings of the variable annuity portfolio.