Choudhry. Fixed Income Securities Derivatives Handbook
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Microsoft Excel Calculation of Vanilla Option Price
CELL C D
8 Underlying price, S 100
9 Volatility % 0.0691
10 Option maturity years 0.25
11 Strike price, X 99.50
12 Risk-free interest rate % 0.05
13
14
15 CELL FORMULAE:
16 ln (S /X ) 0.0050125418 =LN (D8/D11)
17 Adjusted return 0.0000456012500 =((D12-D9)^2/ 2)*D10
18 Time adjusted volatility 0.1314343943 =(D9*D10)^0.5
19 d
2
0.0384841662 =(D16+D17)/D18
20 N (d2) 0.5153492331 =NORMSDIST(D19)
21
22 d
1
0.1699185605 =D19+D18
23 N (d1) 0.5674629098 =NORMSDIST(D22)
24 e
-rt
0.9875778005 =EXP(-D10*D12)
25
26 CALL 6.1060184985 =D8*D23-D11*D20*D24
27 PUT 4.3700096476 * =D26-D8+D11*D24
* By put-call parity, P = C - S + Xe
-rt
332 Appendix
333
REFERENCES
Chapter 1—The Bond Instrument
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Fabozzi, F. 1993. Bond Markets, Analysis and Strategies, 2nd ed. New York:
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Campbell, J. 1986. A Defense of Traditional Hypotheses About the Term Struc-
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Chen, R-R, and L. Scott. 1992. Pricing Interest Rate Options in a Two-Factor
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Contingent Claims. Journal of Finance, December, 1011–1029.
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of Financial Studies, 573–592.
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& Littlefi eld.
James, J., Webber, N. 2000. Interest Rate Modeling. Chichester: John Wiley &
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Princeton: McGraw-Hill.
Merton, R. 1993. Continuous Time Finance. Oxford: Blackwell, chap. 11.
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chap. 5.
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of Financial Economics, 5, 177–188.
Chapter 5—Fitting the Yield Curve
Anderson, N., F. Breedon, M. Deacon, A. Derry, and M. Murphy. 1996. Estimat-
ing and Interpreting the Yield Curve. Chichester: John Wiley & Sons.
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Interest Rates. Journal of Finance, September, 1067–1083.
Choudhry, M., D. Joannas, R. Pereira, and R. Pienaar. 2001. Capital Market
Instruments: Valuation and Analysis. London: FT Prentice Hall.
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Bank of England Working Paper No 24, July.
Gujarati, D. 1995. Basic Econometrics, 3rd ed. New York: McGraw-Hill.
James, J., and N. Webber. 2000. Interest Rate Modeling. Chichester: John Wiley
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and Confi dence Intervals. Journal of Business Finance and Accounting 18,
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Vasicek, O., and H. G. Fong. 1982. Term Structure Modeling Using Exponential
Splines. Journal of Finance 37(2), May, 339–348.
Chapter 6—Forwards and Futures Valuation
For descriptions and analyses of bond futures contracts, basis, implied repo, and the
cheapest-to-deliver bond, see Burghardt et al. (1994). Plona (1996) is a readable
treatment of the European government bond basis.
Burghardt, G. 1994. The Treasury Bond Basis. New York: Irwin.
French, K. 1983. A Comparison of Futures and Forwards Prices. Journal of Finan-
cial Economics 12, November, 311–342.
Galitz, L. 1995. Financial Engineering. London: FT Pitman, chap. 3, 4, 6–8.
Grinblatt, M., and N. Jegadeesh. 2000. Futures vs. Forward Prices: Implica-
tions for Swap Pricing and Derivatives Valuation. In Jegadeesh, N., and
B. Tuckman, eds. Advanced Fixed-Income Valuation Tools. New York: John
Wiley & Sons.
Hull, J. 2000. Options, Futures and Other Derivatives, 4th ed. New York: Prentice
Hall.
Jarrow, R., and G. Oldfi eld. 1981. Forward Contracts and Futures Contracts.
Journal of Financial Economics 9, December, 373–382.
Kolb, R. 2000. Futures, Options and Swaps, 3rd ed. Oxford: Blackwell.
Park, H., and A. Chen. 1985. Differences Between Futures and Forward Prices:
A Further Investigation of Marking to Market Effects. Journal of Futures
Markets 5, February, 77–88.
Plona, C. 1996. The European Bond Basis. New York: McGraw-Hill.
Rubinstein, M. 1999. Rubinstein on Derivatives. London: RISK Books.
Chapter 7—Swaps
Bicksler, J., and A. Chen. 1986. An Economic Analysis of Interest Rate Swaps.
Journal of Finance 41: 3. 645–655.
Brotherton-Ratcliffe, R., and B. Iben. 1993. Yield Curve Applications of Swap
Products. In Schwartz, R., and C. Smith, eds. Advanced Strategies in Financial
Risk Management. New York: New York Institute of Finance.
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338 References
Fabozzi, F., ed. 1998. Perspectives on Interest Rate Risk Management for Money
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Henna, P. 1991. Interest-Rate Risk Management Using Futures and Swaps. Chicago:
Probus.
International Swaps and Derivatives Association. 1991. Code of Standard Work-
ing, Assumptions, and Provisions for Swaps. New York.
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Turnbull, S. 1987. Swaps: A Zero Sum Game. Financial Management 16, Spring,
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Chapter 8—Options
For a detailed discussion of the mathematical basis of the Black-Scholes model, readers
should refer to the original account in Black and Scholes (1973); other good accounts
are in Ingersoll (1987), Neftci (1996), and Nielsen (1999).
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Exotic Derivatives. Chichester: John Wiley and Sons.
Choudhry, M. 2001. The Bond and Money Markets: Strategy, Trading, Analysis.
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Cox, D., and H. Miller. 1965. The Theory of Stochastic Processes. Oxford: Chapman
& Hall.
Cox, J., S. Ross. 1976. The Valuation of Options for Alternative Stochastic Pro-
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Harrison, J., and S. Pliska. 1981. Martingales and Stochastic Integrals in the
Theory of Continuous Trading. Stochastic Processes and Their Applications 11,
216–260.
Haug, E. G. 1998. The Complete Guide to Option Pricing Formulas. Princeton:
McGraw-Hill.
Heston, S. 1993. A Closed Form Solution for Options With Stochastic Volatility
With Application to Bond and Currency Options. Review of Financial Studies
6, 327–343.
Heston, S. 1993. Invisible Parameters in Option Prices. Journal of Finance 48 (3),
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Hull, J., and A. White. 1987. The Pricing of Options on Assets With Stochastic
Volatilities. Journal of Finance 42, 281–300.
Hull, J., and A. White. 1988. An Analysis of the Bias Caused by a Stochastic Vola-
tility in Option Pricing. Advances in Futures and Options Research 3, 29–61.
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Society 4, 1–51.
Klemkosky, R., and B. Resnick. 1979. Put-Call Parity and Market Effi ciency.
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Merton, R. 1973. Theory of Rational Option Pricing. Bell Journal of Economics
and Management Science 4, Spring, 141–183.
———. 1976. Option Pricing When Underlying Stock Returns Are Discon-
tinuous. Journal of Financial Economics 3, Jan–Mar, 125–144.
Neftci, S. 1996. An Introduction to the Mathematics of Financial Derivatives.
Oxford: Academic Press.
Nielsen, L. T. 1999. Pricing and Hedging of Derivative Securities. Oxford: Oxford
University Press.
Rendleman, R., and B. Bartter. 1979. Two State Option Pricing. Journal of
Finance 34, 1092–1110.
Rubinstein, M. 1985. Nonparametric Tests of Alternative Option Pricing Models.
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Scott, L. 1987. Option Pricing When the Variance Changes Randomly. Journal of
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An Analytic Approach. Review of Financial Studies 4, 113–135.
Whaley, R. 1981. On the Valuation of American Call Options on Stocks with
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Chapter 9—Measuring Option Risk
Hull, J. 2000. Options, Futures and Other Derivatives, 4th ed. Princeton: Prentice
Hall.
Kolb, R. 2000. Futures, Options and Swaps, 3rd ed. Oxford: Blackwell.
Galitz, L. 1995. Financial Engineering, rev. ed. London: FT Pitman.
Marshall, J., and V. Bansal. 1992. Financial Engineering. New York: New York
Institute of Finance.
Tucker, A. 1991. Financial Futures, Options and Swaps. Eagan, MN: West
Publishing.
Chapter 10—Credit Derivatives
Bessis, J. 1998. Risk Management in Banking. Chichester: John Wiley & Sons,
17–18.
Crosbie, P. 1997. Modeling Default Risk. Credit Derivatives: Key Issues. London:
British Bankers Association.
Das, S. 1995. Credit Risk Derivatives. Journal of Derivatives, Spring, 7–23.
Das, S. 1997. Credit Derivatives: Products, Applications and Pricing. Singapore:
John Wiley & Sons.
Francis, J., J. Frost, and J. G. Whittaker. 1999. The Handbook of Credit Derivatives.
Princeton: McGraw-Hill.
Das, S., and P. Tufano. 1996. Pricing Credit Sensitive Debt When Interest Rates,
Credit Ratings and Credit Spreads Are Stochastic. Journal of Financial Engi-
neering 5, 161–198.
Gup, B., and R. Brooks. 1993. Interest Rate Risk Management. New York: Irwin.
Jarrow, R., and S. Turnbull. 1996. Credit Risk. In Alexander, C., ed. Handbook of
Risk Management and Analysis. New York: John Wiley & Sons.
Kasapi, A. 1999. Mastering Credit Derivatives. London: FT Prentice Hall, chap. 4.
Longstaff, F., and E. Schwartz. 1995. Valuing Credit Derivatives. Journal of Fixed
Income June, 6–14.
Lucas, D. 1995. Default Correlation and Credit Analysis. Journal of Fixed Income
June 32–41.
Pierides, Y. 1997. The Pricing of Credit Risk Derivatives. Journal of Economic
Dynamics and Control 5, 1579–1611.
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of Lending and Credit Risk Management May, 15–25.
Whittaker, G., and S. Kumar. 1996. Credit Derivatives: A Primer. In Dattatreya,
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340 References
Chapter 11—The Analysis of Bonds with Embedded Options
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of the Call Provision on a Bond. Journal of Finance 33, 1187–2000.
Choudhry, M. 2001. The Bond and Money Markets. London: Butterworth-
Heinemman.
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niques, 3rd ed. Princeton: McGraw-Hill, chap. 16.
Kalotay, A., G. O. Williams, and F. J. Fabozzi. 1993. A Model for the Valuation
of Bonds and Embedded Options. Financial Analysts Journal, May–June,
35–46.
Kish, R., M. Livingstone. 1992. The Determinants of the Call Feature on Corpo-
rate Bonds. Journal of Banking and Finance 16, 687–703.
Livingstone, M. 1993. Money and Capital Markets, 2nd ed. New York: NYIOF.
Mitchell, K. 1991. The Call, Sinking Fund, and Term-to-Maturity Features of
Corporate Bonds: An Empirical Investigation. Journal of Financial and Quan-
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Chichester: John Wiley & Sons, chap. 8.
Tuckman, B. 1996. Fixed Income Securities. New York: John Wiley & Sons, chap. 17.
Van Horne, J. C. 1986. Financial Management and Policy. New York: Prentice
Hall.
Windas, T. 1996. An Introduction to Option-Adjusted Spread Analysis. Princeton:
Bloomberg Press.
Chapter 12—Infl ation-Indexed Bonds
In addition to the references below, Bloomberg users can type ILB <go> 99 <go> to see
illustrations of yield and other calculations on U.S. TII securities.
Anderson, N., F. Breedon, M. Deacon, A. Derry, and J. Murphy. 1996. Estimating
and Interpreting the Yield Curve. Chichester: John Wiley & Sons.
Arak, M., and L. Kreicher. 1985. The Real Rate of Interest: Inferences From the
New U.K. Indexed Gilts. International Economic Review (26) 2, 399–408.
Bootle, R. 1991. Index-Linked Gilts: A Practical Investment Guide, 2nd ed. Cambridge:
Woodhead-Faulkner.
Brown, R., and S. Schaefer. 1994. The Term Structure of Real Interest Rates
and the Cox, Ingersoll and Ross Model. Journal of Financial Economics 35:1,
3–42.
Brynjolfsson, J., and F. Fabozzi. 1999. Handbook of Infl ation Indexed Bonds. New
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