18.5, 18.6, 18.9, and 18.10. Many different charts can be displayed in all three worksheets. Todisplay a chart, you must first choose the variable you require on the vertical axis, the variable yourequire on the horizontal axis, and the range of values to be considered on the horizontal axis.Following that you should hit Enter on your keyboard and click on Draw Graph.
Note that, whenever the values in one or more cells are changed, it is necessary to hit Enter onyour keyboard before clicking on onc of the buttons.
If you have a version of Excel later than 7.0, you will be asked whether you want to update to thenew version when you first save the software. You should choose the Yes button.
Options on Stocks, Currencies, Indices, and Futures
The first worksheet (Equity_FX_Index_Futures) is used for options on stocks, currencies, indices,and futures. To use it, you should first select the Underlying Type (Equity, Currency, Index, orFutures). You should then select the Option Type (Analytic European, Binomial European,Binomial American, Asian, Barrier Up and In, Barrier Up and Out, Barrier Down and In, BarrierDown and Out, Binary Cash or Nothing, Binary Asset or Nothing, Chooser, Compound Option onCall, Compound Option on Put, or Lookback). Finally, enter the data on the underlying asset anddata on the option. Note that all interest rates are expressed with continuous compounding.
In the case of European and American equity options, a table pops up allowing you to enterdividends. Enter the time of each ex-dividend date (in years) in the first column and the amount ofthe dividend in the second column. Dividends must be entered in chronological order.
You must click on buttons to choose whether the option is a call or a put and whether you wishto calculate an implied volatility. If you do wish to calculate an implied volatility, the option priceshould be entered in the cell labeled Price.
Once all the data has been entered you should hit Enter on your keyboard and click onCalculate. If Implied Volatilit d, DerivaGem displays the implied volatility in theVolatility (% per year) eal ed Voi was not selected, it uses the volatility you enteredin this cell and displays the option price in the Price cell.
Once the calculations have been completed, the tree (if used) can be inspected and charts can bedisplayed.
When Analytic European is selected, DerivaGem uses the equations in Chapters 12 and 13 tocalculate prices, and the equations in Chapter 14 to calculate Greek letters. When BinomialEuropean or Binomial American is selected, a binomial tree is constructed as described in Sections18.1 to 18.3. Up to 500 time steps can be used.
The input data are largely self-explanatory. In the gase of an Asian option, the Current Averageis the average price since inception. If the Asian option is new (Time since Inception equals zero),then the Current Average cell is irrelevant and can be left blank. In the case of a Lookback Option,the Minimum to Date is used when a Call is valued and the Maximum to Date is used when a Putis valued. For a new deal, these should be set equal to the current price of the underlying asset.DerivaGem 717
Bond Options
The second worksheet (Bond_Options) is used for European and American options on bonds. Youshould first select a pricing model (Black European, Normal-Analytic European, Normal-TreeEuropean, Normal American, Lognormal European, or Lognormal American). You should thenenter the Bond Data and the Option Data. The coupon is the rate paid per year and the frequency ofpayments can be selected as Quarterly, Semi-Annual or Annual. The zero-coupon yield curve isentered in the table labeled Term Structure. Enter maturities (measured in years) in the first columnand the corresponding continuously compounded rates in the second column. The maturities shouldbe entered in chronological order. DerivaGem assumes a piecewise linear zero curve similar to thatin Figure 5.1. Note that, when valuing interest rate derivatives, DerivaGem rounds all times to thenearest whole number of days.
When all data have been entered, hit Enter on your keyboard. The quoted bond price per $100of Principal, calculated from the zero curve, is displayed when the calculations are complete. Youshould indicate whether the option is a call or a put and whether the strike price is a quoted (clean)strike price or a cash (dirty) strike price. (See the discussion and example in Section 22.2 tounderstand the difference between the two.) Note that the strike price is entered as the price per$100 of principal. You should indicate whether you are considering a call or a put option andwhether you wish to calculate an implied volatility. If you select implied volatility and the normalmodel or lognormal model is used, DerivaGem implies the short rate volatility keeping thereversion rate fixed.
Once all the inputs are complete, you should hit Enter on your keyboard and click Calculate.After that the tree (if used) can be inspected and charts can be displayed. Note that thé tree.displayed lasts until the end of the life of the option. DerivaGem uses a much larger tree in itscomputations to value the underlying bond.
Note that, when Black’s model is selected, DerivaGem uses the equations in Section 22.1.Also, the procedure in Section 22.2 is used for converting the input yield volatility into a pricevolatility.
Caps and Swap Options
The third worksheet (Caps_and_Swap_Options) is used for caps and swap options. You shouldfirst select the Option Type (Swap Option or Cap/Floor) and Pricing Model (Black, NormalEuropean, or Normal American). You should then enter data on the option you are considering.The Settlement Frequency indicates the frequency of payments and can be Annual, Semi-Annual,Quarterly, or Monthly. The software calculates payment dates by working backward from the endof the life of the cap or swap option. The initial accrual period may be a nonstandard lengthbetween 0.5 and 1.5 times a normal accrual period. The software can be used to imply either avolatility or a cap rate/swap rate from the price. When a normal model or a lognormal model isused, DerivaGem implies the short-rate volatility keeping the reversion rate fixed. The zero-couponyield curve is entered in the table labeled Term Structure. Enter maturities (measured in years) inthe first column and the corresponding continuously compounded rates in the second column. Thematurities should be entered in chronological order. DerivaGem assumes a piecewise linear zerocurve similar to that in Figure 5.1.
Once all the inputs are complete, you should click Calculate. After that, charts can bedisplayed.
Note that when Black’s model is used, DerivaGem uses the equations in Sections 22.3 and 22.4.718 DerivaGem
Greek Letters
In the Equity_FX_Index_Futures worksheet, the Greek letters are calculated as follows.Delta: Change in option price per dollar increase in underlying assetGamma: Change in delta per dollar increase in underlying asset
Vega: Change in option price per 1% increase in volatility (e.g., volatility increases from 20%to 21%)
Rho: Change in option price per 1% increase in interest rate (e.g., interest increases from 5%to 6%)
Theta: Change in option price per calendar day passing
In the Bond_Options and Caps_and_Swap_Options worksheets the Greek letters are calculated asfollows:
DVOI: Change in option price per one basis point upward parallel shift in the zero curve
Gamma01: Change in DVO1 per one basis point upward parallel shift in the zero curve,multiplied by 100
Vega: Change in option price when volatility parameter increases by 1% (e.g., volatilityincreases from 20% to 21%)
THE APPLICATIONS BUILDER
 
 
The Applications Builder is DG150functions.xls. It is a set of 21 functions and 7 sampleapplications from which users can build their own applications.
The Functions
The following is a list of the 21 functions included in the Applications Builder. Full details are onthe first worksheet (FunctionSpecs).
1. Black_Scholes. This carries out Black-Scholes calculations for a European option on astock, stock index, currency or futures contract.
2. TreeEquityOpt. This carries out binomial tree calculations for a European or Americanoption on a stock, stock index, currency, or futures contract.
3. BinaryOption. This carries out calculations for a binary option on a stock, stock index,currency, or futures contract.
4. BarrierOption. This carries out calculations for a barrier option on a non-dividend-payingstock, stock index, currency, or futures contract.
5. AverageOption. This carries out calculations for an Asian option on a non-dividend-payingstock, stock index, currency, or futures contract.
6. ChooserOption. This carries out calculations for a chooser option on a non-dividend-paying stock, stock index, currency, or futures contract.
7. CompoundOption. This carries out calculations for compound options on non-dividend-paying stocks, stock indices, currencies, and futures.DerivaGem 719
 
8. LookbackOption. This carries out calculations for a lookback option on a non-dividend-paying stock, stock index, currency, or futures contract.
9. EPortfolio. This carries out calculations for a portfolio of options on a stock, stock index,currency, or futures contract.
10. BlackCap. This carries out calculations for a cap or floor using Black’s model.
11. HullWhiteCap. This carries out calculations for a cap or floor using the Hull-White model.
12. TreeCap. This carries out calculations for a cap or floor using a trinomial tree.
13. BlackSwapOption. This carries out calculations for a swap option using Black’s model.
14. HullWhiteSwap. This carries out calculations for a swap option using the Hull—-Whitemodel.
15. TreeSwapOption. This carries ont calculations for a swap option using a trinomial tree.
16. BlackBondOption. This carries out calculations for a bond option using Black’s model.
17. HullWhiteBondOption. This carries out calculations for a bond option using the Hull-White model.
18. TreeBondOption. This carries out calculations for a bond option using a trinomial tree.
19. BondPrice. This values a bond.
20. SwanPrice. This values a plain vanillov. SWaprrice. i fis Vales &@ Puain vans
arising from reset dates prior to start
a ©mae:t¢.¢on
ime.
21. [Portfolio. This carries out calculations for a portfolio of interest rate derivatives.
Sample ApplicationsDG1S0functions.xls includes seven worksheets with sample applications:A. Binomial Convergence. This investigates the convergence of the binomial model inChapters 10 and 18.B. Greek Letters. This provides charts showing the Greek letters in Chapter 14.. Delta Hedge. This investigates the performance of delta hedging as in Tables 14.2 and 14.3.
D. Delta and Gamma Hedge. This investigates the performance of delta plus gamma hedgingfor a position in a binary option.
QO
E. Value and Risk. This calculates value at risk for a portfolio consisting of three options on asingle stock using three different approaches.
F. Barrier Replication. This carries out calculations for the static options replication example inSection 19.4.
G. Trinomial Convergence. This investigates the convergence of the trinomial tree model in
Chapter 23. -
 MAJOR EXCHANGES TRADINGFUTURES AND OPTIONS
 
Amsterdam ExchangesAmerican Stock ExchangeAustralian Stock ExchangeBrussels ExchangesBolsa de Mercadorias y Futuros, BrazilChicago Board of TradeChicago Board Options ExchangeChicago Mercantile ExchangeCoffee, Sugar & Cocoa Exchange, New YorkCommodity Exchange, New YorkCopenhagen Stock ExchangeDeutsche Termin Borse, GermanyEurexHong Kong Futures ExchangeInternational Petroleum Exchange, LondonKansas City Board of TradeKuala Lumpur Options and FinancialFutures ExchangeLondon International FinancialFutures & Options ExchangeLondon Metal ExchangeMarché a Terme International de FranceMarché des Options Négociables de ParisMEFF Renta Fija and Variable, SpainMidAmerica Commodity ExchangeMinneapolis Grain ExchangeMontreal ExchangeNew York Board of TradeNew York Cotton ExchangeNew York Futures ExchangeNew York Mercantile ExchangeNew York Stock ExchangeNew Zealand Futures & Options Exchange
720
AEXAMEXASXBXSBM&FCBOTCBOECMECSCECOMEX
mniTopPULUL
DTBEUREXHKFEIPEKCBT
KLOFFE
LIFFELMEMATIFMONEPMEFFMidAmMGEMENYBOTNYCENYFENYMEXNYSENZFOE
www.aex.nlWwiw.amex.comwww.asx.com.auwww. bxs.bewww.bmf.com.brWww.chot.comwww.cboe.comwww.cme.comWWwWw.csce.comwww.nymex.comwww.xcse.dkwww.exchange.dewww.eurexchange.comwww.hkfe.com
www.ipe.uk.comwww.kcbt.com
www.kloffe.com.my
www. liffe.comwww.lme.co.ukwww.matif.frwww.monep. frwww.meff.eswww.midam.com
www,.ingex.comwww.me.orgwww.nybot.comwww.nyce.comwww.nyce.comWwww.nymex.com
www.nyse.comwww.nzfoe.com
(continued on next page)Glossary of Notation 721
(continued)
Osaka Securities Exchange ” OSA WwWww.ose.or.jpPacific Exchange PXS www.pacificex.comPhiladelphia Stock Exchange PHLX www.phix.comSingapore International Monetary Exchange SIMEX WWw.simex.com.sgStockholm Options Market OM www.omgroup.comSydney Futures Exchange SFE www.sfe.com.auTokyo Grain Exchange TGE www.tge.or.jpTokyo International Financial Futures Exchange TIFFE www.tiffe.or.jp‘Yoronto Stock Exchange TSE www.tse.comWinnipeg Commodity Exchange WCE www.wce.mb.ca
A number of exchanges have merged or formed alliances. For example:
1. Eurex is an alliance of DTB, CBOT, and exchanges in Switzerland and Finland.
2. MEFF, CME, BM&F, ME, the Paris Bourse (which includes MATIF and MONEP), andthe Singapore Derivatives Exchange (part of SIMEX) have formed the GLOBEX alliance(www.globexalliance.com).
3. In September 2000, AEX, BXS, and the Paris Bourse (which includes MATIF and MONEP)announced that they were forming Euronext.AUTHOR INDEX
 
Abramowitz, M., 248
Aitchison, J., 236
Allen, S. L., 119
Altman, E. 1., 620, 633
Amin, K., 290, 589
Amran, M., 676
Anderson, L. B. G., 460, 477, 478, 479, 585, 586,589
Andreasen, J., 585, 586
Antikarov, V., 676
Arditti, F., 684
Artzner, P., 347
Asay, M., 325
Babbs, S., 465
Bakshi, G., 341
Bardhan, I., 470
Barone-Adesi, G., 427, 429
Bartter, B., 214, 428, 538, 567
Baxter, M., 500
Beaglehole, D. R., 683, 684
Becker, H. P., 198
Bhattacharya, M., 181
Bicksler, J., 147
Biger, N., 290
Black, F., 234, 249, 255, 258, 287, 290, 341, 479,531, 563, 567, 633
Blattberg, R., 257
Bodurtha, J. N., 290, 342
Bollerslev, T., 376, 388
Bookstaber, R. M., 198, 325
Boudoukh, J., 364
Box, G. E. P., 389
Boyle, P. P., 324, 428, 467, 479
Brace, A., 577, 589
Brealey, R. A., 229
Breeden, M., 342
Brennan, M. J., 429, 543, 567
Brenner, M., 290
Broadie, M., 428, 429, 440, 442, 449, 478
Brotherton-Ratcliffe, R., 416, 429, 460, 479, 531
Brown, J. A. C., 236
Buhler, W., 589
Burghardt, G., 567
Cai, L., 684
Canter, M. S., 684
Cao, C., 341
Cao, M., 684
Carabini, C., 64
Carr, P., 429
Carverhill, A., 589
Chance, D. M., 38, 164, 290, 342, 606
Chang, E, C., 64
Chen, A. H., 64, 147
Chen, Z., 341
Cheuk, T. H. F., 465
Cheyette, O., 589
Chiang, R., 119
Chiras, D., 342
Chriss, N., 350
Clewlaw, L., 428, 450, 684
Cole, J. B., 684
Conze, A., 479
Cooper, I., 655
Cootner, P. H., 229
Copeland, T., 676
Cornell, B., 64
Courtadon, G. R., 290, 342, 429, 567
Cox, D. R., 229
Cox, J. C., 64, 68, 164, 214, 258, 392, 428, 456,479, 500, 542, 558, 567, 633, 664
Culp, C., 87, 88
Cumby, R., 389
Curran, M., 416, 429, 450
Das, S., 655
Dattatreya, R. E., 147
Degler, W. H., 198
725726
Author Index
 
Delbaen, F., 347
Demeterfi, K., 606
Derman, E., 337, 342, 447, 450, 460, 461, 470, 479,563, 567, 606
Ding, C. G., 457
Dowd, K., 364
Drezner, Z., 266
Duan, J.-C., 459, 479
Duffie, D., 38, 82, 364, 500, 571, 589, 633, 656
Dumas, B., 342
Dunbar, N., 695
Dupire, B., 460, 479
Dusak, K., 64
Easterwood, J. C., 119
Eber, J. M., 347
Edelberg, C., 325
Ederington, L. H., 88, 198
Emanuel, D., 324
Embrechts, P., 359, 364
Engle, R. F., 374, 376, 380, 387, 389
Ergener, D., 447, 450, 470
Etzioni, E. S., 325
Evnine, J., 479
Eydeland, A., 684
Fabozzi, F. J., 119
Fama, E. E., 251, 257, 258
Feller, W., 229
Fernandes, C., 653, 656
Figlewski, S., 119, 324, 389, 409, 428, 471, 479
Finger, C. C., 633
Flannery, B. P., 379, 416, 417, 429, 565
Fleming, J., 342
Franckle, C. T., 88
French, D. W., 252
French, K. R., 64, 251, 258
Frye, J., 361, 364
Galai, D., 181, 249, 324, 342
Gao, B., 409, 428, 471, 479
Garman M. B., 290, 342, 441, 450, 500
Gatarek, D., 577, 589
Gatto, M. A., 441, 450
Gay, G. D., 119
Geman, H., 684
Geske, R., 255, 258, 429, 437, 450
Gibbs, S., 479
Glasserman, P., 428, 429, 440, 442, 449
Goldman, B., 441, 450
Gonedes, N., 257
Gould, J. P., 181
Grabbe, J. O., 290
Gray, R. W., 64
Hanley, M., 684
Harrison, J. M., 501
Harvey, C. R., 342
Hasbrook, J., 389
Heath, D., 347, 575, 589
Hendricks, D., 364
Hennigar, E., 119
Heston, S. L., 459, 479
Hicks, J. R., 38
Hilliard, J. E., 290
Ho, T. S. Y., 429, 544, 567
Hopper, G., 364
Horn, F. F., 38
Hoskins, B., 567
Hotta, K., 147
Houthakker, H. S., 64
Hua, P., 365
Huang, M., 656
Hudson, M., 450
Hull, J. C., 147, 290, 318, 325, 333, 365, 406, 415,425, 428, 429, 459, 461, 462, 472, 473, 479,480, 501, 546, 552, 558, 560, 564, 567, 568,571, 580, 582, 585, 589, 630, 633, 641, 644,656
Hunter, R., 684
Iben, B., 531
Iben, T., 633
Ingersoll, J. E., 64, 68, 500, 542, 558, 567, 652, 664
Inui, K., 590
Itd, K., 226
Jackson, P., 346, 365
Jackwerth, J. C., 342
Jain, G., 429
Jamshidian, F., 359, 365, 501, 540, 567, 577, 590
Jarrow, R. A., 65, 290, 429, 575, 589, 590, 622,633, 636, 656
Jeffrey, A., 590
Johnson, H. E., 256, 429, 450, 656
Johnson, L. L., 88
Johnson, N. L., 358
Jones, F. J., 38
Jorion, P., 365, 695
Joskow, P., 684
“Ju, X., 695
Kamal, M., 606
Kan, R., 571, 589
Kane, A., 389Author Index
Kane, E. J., 65
Kani, L, 447, 450, 460, 461, 470, 479
Kapner, K. R., 147 «
Karasinski, P., 563, 567
Karlin, S., 229
Kemna, A., 443, 450
Kendall, R., 684
Keynes, J. M., 38
Kijima, M., 568, 590, 627, 633
Kleinstein, A. D., 119
Kiemkosky, R. C., 119, 181, 182, 342
Kluppelberg, C., 359, 364
Kohihagen, 8. W., 290
Kolb, R. W., 38, 119, 164
Koller, T., 676
Kon, 8. J., 257
Kopprasch, R. W., 198
Kotz, S., 358
Kou, S. G., 440, 442, 449
Kreps, D. M., 501
Kulatilaka, N., 676
Lando, D., 627, 633, 636
Langsam, J. A., 325
Lasser, D. J., 119
Latainer, G. O., 325
Lau, S. H., 467, 479
Lauterbach, B., 249, 342
Lee, M., 458
Lee, S.-B., 544, 567
Leland, H. E., 325
Levy, E., 450
Li, A., 568
Litterman, R., 633
Litzenberger, R. H., 147, 342, 683, 684
Lyung, G. M., 389
Longstaff, F. A., 474, 480, 543, 567, 586, 590, 675
MacBeth, J. D., 342
MacMillan, L. W., 427, 429
Manaster, S., 342
Margrabe, W., 445, 450
Markowitz, H., 352
Marshall, J. F., 147
Maude, D. J., 346, 365
McCabe, G. M., 88
MeMillan, L. G., 164, 198
Melick, W. R., 342
Mello, A., 655
Merton, R. C., 182, 234, 258, 269, 290, 457, 480,622, 634
727
Merville, L. J., 342
Mezrich, J., 380, 387, 389Mikosch, T., 359, 364Milevsky, M. A., 450
Miller, H. D., 229
Miller, M., 87. 88
Miltersen, K. R., 290, 577, 590Mintz, D., 418
Moon, M., 666, 667, 676Moro, B., 416, 429
Morton, A., 575, 589
Murrin, J., 676
Musiela, M., 577, 589Myneni, R., 429
Nagayama, I., 568
Naik, E., 458
Natenberg, S., 337
Nefici, S., 229
Neison, D., 376, 389
Ng, V., 376, 389
Nikkhah, S., 88
Noh, J., 389
Oldfield, G. S., 65
Pan, J., 364
Papageorgiou, A., 429
Park, H. Y., 64
Paskov, S. H., 429
Pearson, N., 695
Peisser, A. A. J., 568Perraudin, W., 346, 365Pilipovic, D., 682
Pliska, 8. R., 501
Posner, S, E., 450
Press, W. H., 379, 416, 417, 429, 565Pringle, J. J., 147Ramaswamy, K., 290Rebonato, R