Pricing the Quality Option In Treasury Bond Futures1

This article develops a model for pricing the quality option embedded in the Treasury bond futures contract. Since the option value is set relative to a large family of deliverable bond prices, it is important for the theoretical bond prices to match up to the observed prices. Hence an arbitrage-based model is used where the forward rate process is initialized at its current observable value. A model for valuing the quality option in an otherwise identical forward contract is also established. This permits the quality option and marking to market costs to be separately quantified. Support is provided for the common practice of pricing Treasury bond futures contracts as forward contracts with an embedded forward quality option.     

An analysis of the failed municipal bond and note futures contracts

This study analyzes the failure of the municipal bond and municipal note futures contracts. The municipal bond contract is shown to have been the most effective hedge in the municipal market over its tenure. Changes in volume in the municipal bond contract were closely related to changes in the volume in the U.S. Treasury bond futures contract, the spot–municipal‐over‐bonds (MOB) ratio, and visible supply. The failure of the municipal bond contract is mainly attributed to a decrease in trading volume in the U.S. Treasury futures market. This was impacted by the onset of electronic trading, which the municipal futures market was reluctant to embrace. The municipal note contract was a less effective hedge than U.S. Treasury note futures and ten‐year London Interbank Offered Rate swaps. The failure of the municipal note futures contract is attributed to the existence of well‐established alternative hedges, and segmentation in the municipal market. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:656–679, 2008     

Do tax-exempt yields adjust slowly to substantial changes in taxable yields?

This paper examines the profitability of two futures trading strategies: a municipal bond futures contract strategy and a spread strategy consisting of a municipal bond futures contract and a Treasury bond futures contract. Both strategies are designed to exploit a slow municipal yield adjustment following changes in Treasury yields. We find economically significant profits to both strategies. Average holding period returns per trade for both strategies tend to increase with the magnitude of the Treasury yield change. Profit distributions associated with various Treasury yield change thresholds tend to be positively skewed, and median profits are significantly lower than average profits. The profitability results are consistent with slow municipal yield adjustments. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:763–789, 2008     

Options on bond futures: Isolating the risk premium

The introduction of unspanned sources of risk (and frictions) implies that option prices include a risk premium. Prima facie evidence of the existence of risk premia in option prices is contained in the implied volatility smile patterns reported in the literature. This article isolates the risk premium (defined as the simple difference between estimated and observed option prices) on options on U.K. Gilts, German Bunds, and U.S. Treasury bond futures using models that include price jumps and stochastic volatility. This study finds that single and multi‐factor stochastic volatility models with jumps may explain the empirical regularities observed in bond futures. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:169–215, 2003     

Regime‐switching in stock index and Treasury futures returns and measures of stock market stress

We investigate bivariate regime‐switching in daily futures‐contract returns for the US stock index and ten‐year Treasury notes over the crisis‐rich 1997–2005 period. We allow the return means, volatilities, and correlation to all vary across regimes. We document a striking contrast between regimes, with a high‐stress regime that exhibits a much higher stock volatility, a much lower stock–bond correlation, and a higher mean bond return. The high‐stress regime is associated with higher average values of stock‐implied volatility, stock illiquidity, and stock and bond futures trading volume. The lagged implied volatility from equity‐index options is useful in modeling the time‐varying transition probabilities of the regime‐switching process. Our findings support the notions that: (1) stock market stress can have a material influence on Treasury bond pricing, and (2) the diversification benefits of combined stock–bond holdings tend to be greater during times with relatively high stock market stress. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:753–779, 2010     

Multifactor and analytical valuation of treasury bond futures with an embedded quality option

A closed‐form pricing solution is proposed for the quality option embedded in Treasury bond futures contracts, under a multifactor and D. Heath, R. Jarrow, and A. Morton (1992) Gaussian framework. Such an analytical solution can be obtained through a conditioning approximation, in the sense of M. Curran (1994) and L. Rogers and Z. Shi (1995), or via a rank 1 approximation, following A. Brace and M. Musiela (1994). Monte Carlo simulations show that both approximations are extremely accurate and easy to calculate. Application of the proposed pricing model to the EUREX market from January 2000 through May 2004, yields an excellent fit and an insignificant estimate of the quality option magnitude. On average, this delivery option accounts for only of the futures prices. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:275–303, 2007     

ON THE TIMING OPTION IN A FUTURES CONTRACT

The timing option embedded in a futures contract allows the short position to decide when to deliver the underlying asset during the last month of the contract period. In this paper we derive, within a very general incomplete market framework, an explicit model independent formula for the futures price process in the presence of a timing option. We also provide a characterization of the optimal delivery strategy, and we analyze some concrete examples.     

Futures price limit moves as options

This note demonstrates that an asset's price in an environment with price limit rules can be replicated by the price of a portfolio consisting of a riskless asset and two synthetic options. A procedure is developed to unbundle the unobservable option values imbedded in the actual futures price and impute a theoretical true futures price. Using this framework, evidence from the Treasury Bond futures market suggests that theoretical true futures prices diverge from actual futures prices, on average, 3 h prior to the activation of price limit rules, indicating that price limit moves might be predictable. The reversal of both the actual futures prices and the theoretical futures prices back within the limit range after a limit move provides support for the possibility that traders tend to overreact when market prices are near price limits. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:901–913, 2002     

Why do expiring futures and cash prices diverge for grain markets?

In recent years, cash and futures prices have failed to converge at expiration for selected corn, soybean, and wheat commodity contracts. This lack of convergence raises questions about the effectiveness of arbitrage activities, and increases concerns about the usefulness of these contracts for hedging. We describe the delivery process for these contracts, and show that it embeds a valuable real option on the long side—the option to exchange the deliverable for another futures contract. As the relative volatility of cash and futures prices increases, this option increases in value, which disconnects the cash market from the deliverable instrument in a futures contract. Our estimates of this option's value show that it may create significant price divergence. We parameterize an option pricing model using data on these three commodities from 2000 to 2008 and show that the option model fits closely to recent episodes of non‐convergence, which lends support to the importance of real option effects. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark

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How potent are news reversals?: Evidence from the futures markets

A theoretical model is presented, which predicts a heightening in return volatility following a news reversal. A reversal occurs when a value of an economic indicator that is larger than the forecasted value is followed in the following month by a value smaller than the forecasted value, or vice versa. The model also suggests that the effects of a news reversal will be more pronounced early in the monthly macroeconomic news cycle. The predictions of the model for trading activity are less clear. The main predictions of the model were tested employing intraday data for the nearby Treasury bond futures contract. Consistent with the model, the data show significantly greater responses in volatility per standard‐deviation surprise when there is a news reversal, than otherwise. Further, the increased sensitivity in volatility is especially perceptible early in the announcement cycle. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 29:42–73, 2009     

Role of delivery options in basis convergence

The corn futures contract, traded on the Chicago Board of Trade, provides sellers with delivery options about the timing of delivery, the location of delivery, and the grade to be delivered. These options presumably have values that can vary from one delivery month to the next. The joint values of the timing and location options are estimated for each delivery month for the years 1989 through 1997. These estimates are then used in regression models to determine the degree to which they influence basis variability on the first day of the maturity month. Econometric models are also developed to see if the estimated implicit options values are useful in improving the forecasts of basis convergence over the 2‐month period prior to maturity. The results suggested that variation in the delivery options values in the corn futures contract does indeed help explain basis variability on the first day of maturity. An option‐value variable, based on estimated values two months prior to maturity, resulted in occasional, small improvements (from a statistical point of view) in the precision of forecasts. The existence of delivery options increases basis variability at maturity, but it is difficult to use this information to improve forecasts of basis convergence. One limitation of the analysis is that the Chicago cash market had few transactions per day during the sample period, and hence the reported spot prices may be inadequate for making high‐quality estimates of the options values. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:783–809, 2002     

Does deliverability enhance the value of U.S. Treasury bonds?

This study presents the first examination of the value associated with long‐term U.S. Treasury bonds related to their delivery eligibility in the Treasury bond futures market. The opportunity for study has recently become possible given the reduced maturity of Treasury's noncallable bonds in the market. Consistent with rational behavior, deliverable bonds are found to be more valuable than otherwise comparable, ineligible bonds, and the estimated premia are larger than those previously documented for deliverable bills. However, although detectable and statistically significant, the deliverability component of a cash bond's value is somewhat modest in economic terms; some policy implications of this result are discussed. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:264–274, 2008     

The impact of the US stock market opening on price discovery of government bond futures

We examine price discovery in sequential markets for the 10-year US Treasury note, German bund, and UK gilt futures over the period 2010–2017. We find that price discovery increases after the opening of the US stock market. Order flows in the bond futures markets are more informative for permanent price changes in the 30-min period after the US stock market opens. A placebo test using US statutory holidays confirms our findings. A cross-market analysis suggests that the increased price discovery in the bond futures is related to returns and net order flows of the US stock market.     

Price discovery in the options markets: An application of put‐call parity

This study investigates the relative rate of price discovery in Taiwan between index futures and index options, proposing a put‐call parity (PCP) approach to recover the spot index embedded in the options premiums. The PCP approach offers the benefits of reducing model risk and alleviating the burden of volatility estimation. Consistent with the trading‐cost hypothesis, a dominant tendency is found for futures and a subordinate but non‐trivial price discovery from options. The relative weight of options price discovery is sensitive to the methodology employed as the means of inferring the option‐implicit spot price. The empirical evidence suggests that the information contained in the PCP‐implied spot encompasses that provided by the Black‐Scholes‐implied spot. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:354– 375, 2008     

Examination of long‐term bond iShare option selling strategies

This article examines volatility trades in Lehman Brothers 20+ Year US Treasury Index iShare (TLT) options from July 2003 through May 2007. Unconditionally selling front contract strangles and straddles and holding for one month is highly profitable after transactions costs. Short‐term option selling strategies are enhanced when implied volatility is high relative to time series volatility forecasts. Risk management strategies such as stop loss orders detract from profitability, while take profit orders have only modest favorable effects on profitability. Overall, the results demonstrate that TLT option selling strategies offered attractive risk‐return tradeoffs over the sample period. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:465–489, 2010     

Valuing real options using implied binomial trees and commodity futures options

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market‐implied probability distributions for commodity prices. In addition, the existence of long‐dated futures options means that good volatility estimates may now be incorporated into capital budgeting evaluations of real options projects with long planning horizons. An example is given using gold futures options and a real option to extract gold from a mine. A detailed out‐of‐sample test is included that shows how IBT option pricing errors evolve on subtrees emanating from future levels of the underlying asset. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:203–226, 2007     

Implied volatility forecasts in the grains complex

This article finds that the implied volatilities of corn, soybean, and wheat futures options 4 weeks before option expiration have significant predictive power for the underlying futures contract return volatilities through option expiration from January 1988 through September 1999. These implied volatilities also encompass the information in out‐of‐sample seasonal Glosten, Jagannathan, and Runkle (GJR;1993) volatility forecasts. Evidence also demonstrates that when corn‐implied volatility rises relative to out‐of‐sample seasonal GJR volatility forecasts, implied volatility substantially overpredicts realized volatility. However, simulations of trading rules that involve selling corn option straddles when corn‐implied volatility is high relative to out‐of‐sample GJR volatility forecasts indicate that none of the trading rules would have been significantly profitable. This finding suggests that these options are not necessarily overpriced. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:959–981, 2002     

Migration of price discovery in semiregulated derivatives markets

This study investigates the information content of futures option prices when the underlying futures price is regulated and the futures option price is not. The New York Board of Trade (NYBOT) provides the empirical setting for this regulatory mismatch. Many commodity derivatives markets regulate the prices of all derivatives on a single underlying commodity simultaneously. Some exchanges, including the NYBOT, regulate only their futures contracts, leaving the options on these futures contracts unregulated. This study takes a particular interest in the option‐implied futures price when the observed futures price is locked limit. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:209–241, 2006     

Catastrophe futures and reinsurance contracts: An incomplete markets approach

We present a theoretical methodology for the pricing of catastrophe (CAT) derivatives with event‐dependent and non‐convex payoffs given the price of a CAT indexed futures contract. We do not assume a fully diversifiable CAT event risk, nor do we assume knowledge of the martingale probability measure beyond the futures price. We derive tight bounds on the contract value and present trading strategies exploiting the mispricing whenever the bounds are violated. We estimate the bounds of the reinsurance contract with data from hurricane landings in Florida. Our method is also applicable when there is no futures market but the price of a CAT‐indexed bond is available.     

Does maturity matter? The case of treasury futures volume

We find that Treasury futures volume contains information about future economic and financial market conditions. Short- and long-term volumes are economically different: A relatively higher volume in short-term (long-term) Treasury futures is counter-cyclical (procyclical), preceding worse (better) economic and financial conditions. Further, we construct a single factor from futures volumes of different maturities that forecasts the performances of Treasury securities and the corporate debt and equity markets, as well as macroeconomic conditions. Our results are consistent with the notion that futures volumes from different market segments reflect differences in beliefs and contain different information about future financial and economic activity.