Black-Derman-Toy (BDT) Modeling

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.

Heath-Jarrow-Morton (HJM) Modeling

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.

Hull-White (HW) and Black-Karasinski (BK) Modeling

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.

Cox-Ross-Rubinstein (CRR) Modeling

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.

Implied Trinomial Tree (ITT) Modeling

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.

Leisen-Reimer Tree (LR) Modeling

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.

Equal Probabilities Tree (EQP) Modeling

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.

Closed-Form Solutions Modeling

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.

Financial Derivatives

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.

Fitting Interest-Rate Curve Functions

[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.

Interest-Rate Modeling Using Monte Carlo Simulation

[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.

Bootstrapping a Swap Curve

[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.

Bond Futures

[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.

Credit Derivatives

[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.

Convertible Bonds

[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.