Main Content

A description of the Black-Derman-Toy interest-rate model can be found in:

[1] Black, Fischer, Emanuel Derman, and William Toy. “A One Factor Model of
Interest Rates and its Application to Treasury Bond Options.”
*Financial Analysts Journal.* January - February 1990.

An introduction to Heath-Jarrow-Morton modeling, used extensively in Financial Instruments Toolbox™ software, can be found in:

[2] Jarrow, Robert A. *Modelling Fixed Income Securities and Interest
Rate Options.* McGraw-Hill, 1996, ISBN 0-07-912253-1.

A description of the Hull-White model and its Black-Karasinski modification can be found in:

[3] Hull, John C. *Options, Futures, and Other Derivatives.*
Prentice-Hall, 1997, ISBN 0-13-186479-3.

You can find additional information about the Hull-White single-factor model used in this toolbox in these papers:

[4] Hull, J., and A. White. “Numerical Procedures for Implementing Term
Structure Models I: Single-Factor Models.” *Journal of
Derivatives.* 1994.

[5] Hull, J., and A. White. “Using Hull-White Interest Rate Trees.”
*Journal of Derivatives.* 1996.

To learn about the Cox-Ross-Rubinstein model, see:

[6] Cox, J. C., S. A. Ross, and M. Rubinstein. “Option Pricing: A
Simplified Approach.” *Journal of Financial Economics.*
Number 7, 1979, pp. 229–263.

To learn about the Implied Trinomial Tree model, see:

[7] Chriss, Neil A., E. Derman, and I. Kani. “Implied trinomial trees of
the volatility smile.” *Journal of Derivatives.*
1996.

To learn about the Leisen-Reimer model, see:

[8] Leisen D.P., M. Reimer. “Binomial Models for Option Valuation –
Examining and Improving Convergence.” *Applied Mathematical
Finance.* Number 3, 1996, pp. 319–346.

To learn about the Equal Probabilities model, see:

[9] Chriss, Neil A. *Black Scholes and Beyond: Option Pricing
Models.* McGraw-Hill, 1996, ISBN 0-7863-1025-1.

To learn about the Bjerksund-Stensland 2002 model, see:

[10] Bjerksund, P. and G. Stensland. “Closed-Form Approximation of American
Options.” *Scandinavian Journal of Management.* Vol. 9,
1993, Suppl., pp. S88–S99.

[11] Bjerksund, P. and G. Stensland. *“Closed Form Valuation of
American Options.”*, Discussion paper 2002 (https://www.scribd.com/doc/215619796/Closed-form-Valuation-of-American-Options-by-Bjerksund-and-Stensland#scribd)

You can find information on the creation of financial derivatives and their role in the marketplace in numerous sources. Among those consulted in the development of Financial Instruments Toolbox software are:

[12] Chance, Don. M. *An Introduction to Derivatives.* The
Dryden Press, 1998, ISBN 0-030-024483-8.

[13] Fabozzi, Frank J. *Treasury Securities and Derivatives.*
Frank J. Fabozzi Associates, 1998, ISBN 1-883249-23-6.

[14] Wilmott, Paul. *Derivatives: The Theory and Practice of Financial
Engineering.* John Wiley and Sons, 1998, ISBN 0-471-983-89-6.

[15] Nelson, C.R., Siegel, A.F. "Parsimonious modelling of yield curves."
*Journal of Business.* Number 60, 1987, pp 473–89.

[16] Svensson, L.E.O. * "Estimating and interpreting forward interest
rates: Sweden 1992-4."* International Monetary Fund, IMF Working
Paper, 1994, p. 114.

[17] Fisher, M., Nychka, D., Zervos, D. *"Fitting the term structure of
interest rates with smoothing splines.”* Board of Governors of
the Federal Reserve System, Federal Reserve Board Working Paper, 1995.

[18] Anderson, N., Sleath, J. "New estimates of the UK real and nominal yield
curves." *Bank of England Quarterly Bulletin.* November, 1999, pp
384–92.

[19] Waggoner, D. "Spline Methods for Extracting Interest Rate Curves from Coupon Bond Prices," Federal Reserve Board Working Paper, 1997, p. 10.

[20] "Zero-coupon yield curves: technical documentation." *BIS
Papers*, Bank for International Settlements, Number 25, October,
2005.

[21] Bolder, D.J., Gusba,S. "Exponentials, Polynomials, and Fourier Series: More
Yield Curve Modelling at the Bank of Canada." *Working Papers.*
Bank of Canada, 2002, p. 29.

[22] Bolder, D.J., Streliski, D. "Yield Curve Modelling at the Bank of Canada."
*Technical Reports.* Number 84, 1999, Bank of Canada.

[23] Brigo, D. and F. Mercurio. *Interest Rate Models - Theory and
Practice with Smile, Inflation and Credit.* Springer Finance,
2006.

[24] Andersen, L. and V. Piterbarg. *Interest Rate Modeling.*
Atlantic Financial Press. 2010.

[25] Hull, J, *Options, Futures, and Other Derivatives.*
Springer Finance, 2003.

[26] Glasserman, P. *Monte Carlo Methods in Financial
Engineering.* Prentice Hall, 2008.

[27] Rebonato, R., K. McKay, and R. White. *The Sabr/Libor Market Model:
Pricing, Calibration and Hedging for Complex Interest-Rate
Derivatives.* John Wiley & Sons, 2010.

[28] Hagan, P., West, G. "Interpolation Methods for Curve Construction."
*Applied Mathematical Finance.* Vol. 13, Number 2,
2006.

[29] Ron, Uri. "A Practical Guide to Swap Curve Construction." *Working
Papers.* Bank of Canada, 2000, p. 17.

[30] Burghardt, G., T. Belton, M. Lane, and J. Papa. *The Treasury Bond
Basis.* McGraw-Hill, 2005.

[31] Krgin, Dragomir. *Handbook of Global Fixed Income
Calculations.* John Wiley & Sons, 2002.

[32] Beumee, J., D. Brigo, D. Schiemert, and G. Stoyle. “Charting a Course
Through the CDS Big Bang.” *Fitch Solutions, Quantitative
Research.* Global Special Report. April 7, 2009.

[33] Hull, J., and A. White. “Valuing Credit Default Swaps I: No
Counterparty Default Risk.” *Journal of Derivatives.* Vol.
8, pp. 29–40.

[34] O'Kane, D. and S. Turnbull. “Valuation of Credit Default
Swaps.” *Lehman Brothers, Fixed Income Quantitative Credit
Research.* April, 2003.

[35] O'Kane, D. *Modelling Single-name and Multi-name Credit
Derivatives.* Wiley Finance, 2008, pp. 156–169.

[36] Tsiveriotis, K., and C. Fernandes. “Valuing Convertible Bonds with
Credit Risk.” *Journal of Fixed Income.* Vol. 8, 1998,
pp. 95–102.

[37] Hull, J. *Options, Futures and Other Derivatives.*
Fourth Edition. Prentice Hall, 2000, pp. 646–649.