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2015 | OriginalPaper | Buchkapitel

71. Analytical Bounds for Treasury Bond Futures Prices

verfasst von : Ren-Raw Chen, Shih-Kuo Yeh

Erschienen in: Handbook of Financial Econometrics and Statistics

Verlag: Springer New York

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Abstract

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 (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 employs a maximum likelihood estimation technique presented by Chen and Scott (1993) to estimate the parameters for two-factor Cox-Ingersoll-Ross models of the term structure. Following the estimation, the factor values are solved for by matching the short rate with the cheapest-to-deliver bond price. Then, upper bounds and lower bounds for Treasury bond futures prices can be calculated.

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.

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Vorheriges Kapitel Evaluating the Effectiveness of Futures Hedging

Nächstes Kapitel Rating Dynamics of Fallen Angels and Their Speculative Grade-Rated Peers: Static vs. Dynamic Approach

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See, for example, Carr and Chen (1996), Kilcollin (1982), Benninga and Smirlock (1985), Kane and Marcus (1986), and Hedge (1990).

See, for example, Arak and Goodman (1987), Hedge (1988), and Gay and Manaster (1986).

These bounds are not to be violated, or arbitrage profits should take place. As it will become clear (in Sect. 71.4), in the case of the upper bound that is model-free, a simple trading strategy can be formed to arbitrage against the violation (under perfect markets). In the case of the semi-model-dependent lower bound, arbitrage profits exist only if the assumed model is correct.

T bond market is an over the counter market that has no official closing time, even though market practice adopts 3:00 p.m. Eastern time as a symbolic closing time. The futures market allows the short up to 8:00 p.m. Eastern time to make the delivery announcement, and hence theoretically there is a 5-h window for the wild card.

Also see Hull (2009).

For example, the closed-form solution under the one-factor Cox-Ingersoll-Ross model can be found in Carr (1988).

The name “accrued interest” comes in because in the delivery month, the bond price increases due to accrued interests. Here, Q is a traded price that included accrued interests.

If there is a coupon in between t and T, we simply subtract the coupon value from the expected value.

Note that in the second line of Eq. 71.17 where q _i is divided through is due to the fact that there exists a bond i such that max{Φ(u)q _i − δ(t, u + h)Q _i(u + h)} > 0 in all states.

This two-factor model is adopted by a number of authors. See Chen and Scott (1993), Turnbull and Milne (1991), Langetieg (1980), and Hull and White (1990).

T bond futures prices are affected by all bonds underlying the yield curve, and yet doubtlessly the cheapest-to-deliver bond has the most influence.

See, for example, Chen and Scott (1993) and Jagannathan et al. (2003).

All 10 cases are in the second subperiod: 1992–2000.

Chen and Scott (1993) argue that the three-factor model does not necessarily dominate the two-factor model; in that, the three-factor model, although fits better the term structure, generates extra volatility. See Chen and Scott for details.

The result of the alternative fitting is available upon request.

Hull (2009) has an excellent demonstration of such a computation.

That is, we do the business day count between trade day and the last day of the delivery month and assume 252 trading days for a given year.

Lee et al. (2000) provide excellent introductions about how to conduct multiple regressions.

Arak, M., & Goodman, L. (1987). Treasury bond futures: Valuing the delivery option. Journal of Futures Markets, 7(3), 269–286.CrossRef

Benninga, S., & Smirlock, M. (1985). An empirical analysis of the delivery option, marking to market, and the pricing of Treasury bond futures. Journal of Futures Markets, 5(3), 361–374.CrossRef

Boyle, P. (1989). The quality option and timing option in futures contracts. Journal of Finance, 44(1), 101–113.CrossRef

Broadie, M., & Sundaresan, S. (1987) The pricing of timing and quality options: An application to Treasury bond futures markets. Working paper.

Carr, P. (1988) Valuing bond futures and the quality option. Working paper, University of California at Los Angeles.

Carr, P., & Chen, R. (1996). Valuing bond futures and the quality option. Working paper, Rutgers University, November.

Chen, R., & Scott, L. (1993). Maximum likelihood estimation of a multi-factor equilibrium model of the term structure of interest rates. Journal of Fixed Income, 3(3), 14–32.CrossRef

Chen, R., & Yeh, S. K. (2002). Analytical bounds for American option prices. Journal of Financial and Quantitative Analysis, 37(01), 117–135.CrossRef

Cox, J., Ingersoll, J., & Ross, S. (1981). The relation between forward prices and futures prices. Journal of Financial Economics, 9(4), 321–346.CrossRef

Cox, J., Ingersoll, J., & Ross, S. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385–407.CrossRef

Duan, J., & Simonato, J. (1999). Estimating and testing exponential-affine term structure models by Kalman Filter. Review of Quantitative Finance and Accounting, 13, 111–135.CrossRef

Gay, G., & Manaster, S. (1986). Implicit delivery options and optimal delivery strategies for financial futures contracts. Journal of Financial Economics, 16(1), 41–72.CrossRef

Hamiltion, J. (1994). Time series analysis. Princeton: Princeton University Press.

Heath, D., Jarrow, R., & Morton, A. (1992). Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation. Econometrica, 60(1), 77–105.CrossRef

Hedge, S. (1988). An empirical analysis of implicit delivery options in the Treasury bond futures contract. Journal of Banking and Finance, 12(2), 469–492.

Hedge, S. (1990). An ex post valuation of the quality option in Treasury bond futures contract. Journal of Banking and Finance, 14(4), 741–760.CrossRef

Hemler, M. (1990). The quality delivery option in Treasury bond futures contracts. Journal of Finance, 45(5), 1565–1586.CrossRef

Ho, T., Lee, S., & Son, K. (1992). Term structure estimation and pricing of callable Treasury bonds. Review of Quantitative Finance and Accounting, 2(2), 127–143.CrossRef

Hull, J. (2009) Options, futures, and other derivative contracts (7th ed.) Prentice Hall.

Hull, J., & White, A. (1990). Pricing interest-rate-derivative securities. The Review of Financial Studies, 3(4), 573–592.CrossRef

Jagannathan, R., Kaplin, A., & Sun, S. (2003). An evaluation of multi-factor CIR models using LIBOR, swap rates, and cap and swaption prices. Journal of Econometrics, 116, 113–146.CrossRef

Jamshidian, F. (1989). An exact bond option formula. Journal of Finance, 4(1), 205–209.CrossRef

Kane, A., & Marcus, A. (1984). Conversion factor risk and hedging in the Treasury bond futures market. Journal of Futures Markets, 4(1), 55–64.CrossRef

Kane, A., & Marcus, A. (1986). Valuation and optimal exercise of the wild card option in the Treasury bond futures market. Journal of Finance, 41(1), 195–207.CrossRef

Kilcollin, T. (1982). Difference systems in financial futures markets. Journal of Finance, 37(5), 1883–1897.CrossRef

Langetieg, T. (1980). A multivariate model of the term structure. Journal of Finance, 35(1), 71–97.

Lee C., Lee A., & Lee J. (2000). Statistics for business and financial economics (2nd ed). World Scientific Publishers.

Livingston, M. (1987). The delivery option on forward contracts. Journal of Financial and Quantitative Analysis, 22(01), 79–87.CrossRef

Lo, A. W. (1987). Semi-parametric upper bounds for options prices and expected payoffs. Journal of Financial Economics, 19(2), 373–387.CrossRef

Longstaff, F., & Schwartz, E. (1992). Interest rate volatility and the term structure: A two-factor general equilibrium model. Journal of Finance, 47(4), 1259–1282.CrossRef

Margrabe, W. (1978). The value of an option to exchange one asset for another. Journal of Finance, 33, 177–186.CrossRef

Ritchken, P., & Sankarasubramanian, L. (1992). Pricing the quality option in Treasury bond futures. Mathematical Finance, 2(3), 197–214.CrossRef

Turnbull, S., & Milne, F. (1991). A simple approach to interest-rate option pricing. The Review of Financial Studies, 4(1), 87–120.CrossRef

Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.CrossRef

Yeh, S. K., & Lin, B. H. (2003). Term structure fitting and information content: An empirical study on the Taiwanese government bond market. Review of Pacific Basin Financial Markets and Policies, 6(3), 1–44.CrossRef

Zhang, P. G. (1994). Bounds for option prices and expected payoffs. Review of Quantitative Finance and Accounting, 4(2), 179–197.CrossRef

Titel: Analytical Bounds for Treasury Bond Futures Prices
verfasst von: Ren-Raw Chen
Shih-Kuo Yeh
Verlag: Springer New York
Buch: Handbook of Financial Econometrics and Statistics
Print ISBN: 978-1-4614-7749-5

Electronic ISBN: 978-1-4614-7750-1

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-1-4614-7750-1_71