Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-22T19:06:39.071Z Has data issue: false hasContentIssue false
  • English
  • Français

A Discrete Time Model for Pricing Treasury Bills, Forward, and Futures Contracts*

Published online by Cambridge University Press:  29 August 2014

I.G. Morgan  and
E.H. Neave
I.G. Morgan*
Affiliation:
Queen's University School of Business, Kingston, Ontario K7L 3N6
E.H. Neave*
Affiliation:
Queen's University School of Business, Kingston, Ontario K7L 3N6
*
Queen's University School of Business, Kingston, Ontario K7K 3N6.
Queen's University School of Business, Kingston, Ontario K7K 3N6.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper develops a discrete time model for valuing treasury bills and either forward or futures contracts written against them. It provides formulae for bill prices, forward prices, futures prices, and their conditional variances and risk premiums. The interest rate process is described by a multiplicative binomial random walk whose features conform to some principal characteristics of observed processes. Initial forward rates are constrained to match initially observed term structure data.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 23 , Issue 1 , May 1993 , pp. 3 - 22
Copyright
Copyright © International Actuarial Association 1993

Footnotes

*

Earlier versions of this paper were presented to the Inaugural Meetings of the Northern Finance Association, Ottawa, Canada, September 23-24, 1989, and to the First AFIR International Colloquium of the International Actuarial Association, Paris, April 23-27, 1990. We thank the editor and referees for constructive suggestions.

References

REFERENCES

Black, F, (1976) The pricing of commodity contracts. Journal of Financial Economics 3, 167–179.CrossRefGoogle Scholar
Black, F., Derman, E. and Toy, W. (1990) A one-factor model of interest rates and its application to treasury bill options. Financial Analysts Journal, January-February, 33–39.Google Scholar
Bliss, R.R. and Ronn, E.I. (1989) Arbitrage-based estimation of nonstationary shifts in the term structure of interest rates. Journal of Finance 44, 591–610.Google Scholar
Boyle, P.B. (1989) The quality option and timing option in futures contracts. Journal of Finance 44, 101–113.CrossRefGoogle Scholar
Cox, J. C., Ingersoll, J. and Ross, S.A. (1981) The relation between forward prices and futures prices. Journal of Financial Economics 9, 321–346.CrossRefGoogle Scholar
Cox, J.C. and Rubinstein, M. (1985) Options Markets, Englewood Cliffs, N.J.Prentice-Hall.Google Scholar
Cox, J.C., Ross, S.A. and Rubinstein, M. (1979) Option pricing: a simplified approach. Journal of Financial Economics 7, 229–263.CrossRefGoogle Scholar
Dybvig, P.H. (1989) Bond and bond option pricing based on the current term structure, manuscript.Google Scholar
Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.CrossRefGoogle Scholar
Engle, R.F., Lilien, D.M. and Robins, R.P. (1987) Estimating time varying risk premia in the term structure. Econometrica 55, 391–407.CrossRefGoogle Scholar
French, K.R. (1981) A comparison of futures and forward prices. Journal of Financial Economics 12, 311–342.CrossRefGoogle Scholar
Gay, G.D. and Manaster, S. (1984) The quality option implicit in futures contracts. Journal of Financial Economics 13, 353–370.CrossRefGoogle Scholar
Heath, D., Jarrow, R. and Morton, A. (1992) “Bond pricing and the term structure of interest rates”. Econometrica 60, 77–105.CrossRefGoogle Scholar
Heath, D., Jarrow, R. and Morton, A. (1990a) “Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation”. Journal of Financial and Quantitative Analysis 25, 419–440.CrossRefGoogle Scholar
Heath, D., Jarrow, R. and Morton, A. (1990b) “Contingent Claim Valuation with a Random Evolution of Interest Rates”. The Review of Futures Markets 9, 54–76.Google Scholar
Hemler, M.L.The quality delivery option in treasury bond futures contracts. Journal of Finance 45, 1565–1586.CrossRefGoogle Scholar
Ho, T.S.Y. and Lee, S. (1986) Term structure movements and pricing interest rate contingent claims. Journal of Finance 41, 1011–1029.CrossRefGoogle Scholar
Huang, C-f and Litzenberger, R.H. (1988) Foundations for financial economics. North-Holland.Google Scholar
Hull, J. and White, A. (1989) “Pricing interest-rate sensitive securities”. University of Toronto Graduate School of Management Working Paper, presented to Northern Finance Association,Ottawa, 1989.Google Scholar
Hull, J. and White, A. (1990) One factor interest-rate models and the valuation of interest-rate derivative securities. University of Toronto Working Paper.CrossRefGoogle Scholar
Jacobs, R.L. and Jones, R.A. (1980) The treasury bill futures market. Journal of Political Economy 88, 699–721.CrossRefGoogle Scholar
Jamshidian, F. (1989) An exact bond option formula. Journal of Finance 44, 205–209.CrossRefGoogle Scholar
Jamshidian, F. (1990) Bond and option evaluation in the Gaussian interest model. Research in Finance..Google Scholar
Jamshidian, F. (1990) The preference free determination of bond and option prices from the spot interest rate. In: Advances in Futures and Options Research 4, 51–67.Google Scholar
Jamshidian, F. (1991) Forward induction and construction of yield curve diffusion models. Journal of Fixed Income, 62–74.CrossRefGoogle Scholar
Jarrow, R.A. and Oldfield, G.S. (1981) Forward contracts and futures contracts. Journal of Financial Economics 9, 373–382.CrossRefGoogle Scholar
Kane, A. and Marcus, A. (1986) Valuation and optimal exercise of the wild card option in the treasury bond futures market. Journal of Finance 41, 195–207.CrossRefGoogle Scholar
Kishimoto, N. (1989) Pricing contingent claims under interest rate and asset price risk. Journal of Finance 44, 571–590.CrossRefGoogle Scholar
Morgan, I.G. and Neave, E.H. (1989) A discrete time forward and futures pricing model. Proceedings, First AFIR International Conference, Paris, 1989.Google Scholar
Morgan, I.G. and Neave, E.H. (1991) “A mean reverting process for pricing treasury bills and futures contracts”. Second AFIR International Colloquium, Brighton, vol I, 237–266.Google Scholar
Morgan, I.G. and Neave, E.H. (1992) “Time series properties of futures prices for pure discount bonds”, to be presented to Western Finance Association Meetings, San Francisco.Google Scholar
Newey, W.K. (1985) Maximum likelihood specification testing and conditional moment tests. Econometrica 53, 1047–1070.CrossRefGoogle Scholar
Pagan, A.R. and Sabau, H.C.L. (1987) Consistency test for heteroskedastic and risk models, manuscript.Google Scholar
Pedersen, H.W., Shiu, E.S.W. and Thorlacius, A.E. (1989) Arbitrage-free pricing of interest-rate contingent claims. Transactions of the Society of Actuaries 41, 231–265.Google Scholar
Poitras, G. (1988) “Hedging Canadian Treasury Bill Positions with US Money Market Futures Contracts”;. Review of Futures Markets 7, 176–191.Google Scholar
Richard, S.F. and Sundaresan, M. (1981) A continuous time equilibrium model of forward prices and futures prices in a multigood economy. Journal of Financial Economics 9, 347–372.CrossRefGoogle Scholar
Ritchken, P. and Boenawan, K. (1990) On arbitrage free pricing of interest rate contingent claims: a note. Journal of Finance 45, 259–264.Google Scholar
Ritchken, P. and Sankarasubramanian, L. (1990) On valuing complex interest rate claims. The Journal of Futures Markets 10, 443–455.CrossRefGoogle Scholar
Tauchen, G.E. (1985) Diagnostic testing and evaluation of maximum likelihood models. Journal of Econometrics 30, 415–443.CrossRefGoogle Scholar
Turnbull, S.M. and Milne, F. (1991) A simple approach to interest-rate option pricing. Review of Financial Studies 4, 87–120.CrossRefGoogle Scholar