
List of Business Snapshots 


xvi  


xvii  
Preface 

xix  


1  (20) 


1  (1) 


2  (1) 


3  (3) 


6  (1) 


6  (2) 


8  (1) 


9  (2) 


11  (3) 


14  (1) 


15  (6) 


15  (1) 


16  (1) 


16  (2) 


18  (3) 

Mechanics of futures markets 


21  (26) 


21  (2) 

Specification of a futures contract 


23  (3) 

Convergence of futures price to spot price 


26  (1) 

Daily settlement and margins 


26  (5) 


31  (4) 


35  (1) 

Types of traders and types of orders 


36  (1) 


37  (2) 


39  (1) 

Forward vs. futures contracts 


40  (7) 


41  (1) 


42  (1) 


43  (1) 


44  (3) 

Hedging strategies using futures 


47  (28) 


47  (3) 

Arguments for and against hedging 


50  (3) 


53  (3) 


56  (4) 


60  (7) 

Rolling the hedge forward 


67  (8) 


68  (1) 


69  (1) 


70  (1) 


71  (2) 

Appendix: Proof of the minimum variance hedge ratio formula 


73  (2) 


75  (24) 


75  (2) 


77  (3) 


80  (1) 


80  (2) 

Determining Treasury zero rates 


82  (2) 


84  (3) 


87  (2) 


89  (3) 


92  (1) 

Theories of the term structure of interest rates 


93  (6) 


94  (1) 


95  (1) 


95  (2) 


97  (2) 

Determination of forward and futures prices 


99  (30) 

Investment assets vs. consumption assets 


99  (1) 


99  (2) 


101  (1) 

Forward price for an investment asset 


101  (3) 


104  (3) 


107  (1) 

Valuing forward contracts 


107  (2) 

Are forward prices and futures prices equal? 


109  (1) 

Futures prices of stock indices 


110  (2) 

Forward and futures contracts on currencies 


112  (4) 


116  (2) 


118  (1) 


119  (1) 

Futures prices and expected future spot prices 


119  (10) 


121  (1) 


122  (1) 


123  (2) 


125  (2) 

Appendix: Proof that forward and futures prices are equal when interest rates are constant 


127  (2) 


129  (20) 


129  (2) 

Quotations for Treasury bonds 


131  (2) 


133  (4) 


137  (5) 

Durationbased hedging strategies 


142  (1) 

Hedging portfolios of assets and liabilities 


143  (6) 


144  (1) 


145  (1) 


145  (2) 


147  (2) 


149  (32) 

Mechanics of interest rate swaps 


149  (6) 


155  (1) 


156  (1) 

The comparativeadvantage argument 


157  (3) 


160  (1) 

Determining the LIBOR/swap zero rates 


160  (1) 

Valuation of interest rate swaps 


161  (4) 


165  (3) 

Valuation of currency swaps 


168  (3) 


171  (2) 


173  (8) 


175  (1) 


176  (1) 


176  (2) 


178  (3) 

Mechanics of options markets 


181  (24) 


181  (2) 


183  (2) 


185  (2) 

Specification of stock options 


187  (3) 


190  (2) 


192  (1) 


192  (2) 


194  (1) 

The options clearing corporation 


195  (1) 


196  (1) 


196  (1) 

Warrants, executive stock options, and convertibles 


197  (1) 


198  (7) 


200  (1) 


200  (1) 


201  (1) 


202  (3) 

Properties of stock options 


205  (18) 

Factors affecting option prices 


205  (4) 


209  (1) 

Upper and lower bounds for option prices 


209  (3) 


212  (3) 

Early exercise: calls on a nondividendpaying stock 


215  (1) 

Early exercise: puts on a nondividendpaying stock 


216  (2) 


218  (5) 


219  (1) 


220  (1) 


220  (2) 


222  (1) 

Trading strategies involving options 


223  (18) 

Strategies involving a single option and a stock 


223  (2) 


225  (9) 


234  (3) 


237  (4) 


237  (1) 


238  (1) 


238  (1) 


239  (2) 


241  (22) 


241  (3) 


244  (3) 


247  (2) 


249  (1) 


250  (1) 


251  (1) 

Matching volatility with u and d 


252  (3) 

Increasing the number of steps 


255  (1) 


256  (7) 


260  (1) 


260  (1) 


261  (1) 


262  (1) 

Wiener processes and Ito's lemma 


263  (18) 


263  (1) 

Continuoustime stochastic processes 


264  (5) 

The process for a stock price 


269  (3) 


272  (1) 


273  (1) 


274  (7) 


275  (1) 


276  (1) 


276  (1) 


277  (2) 

Appendix: Derivation of Ito's lemma 


279  (2) 

The BlackScholesMerton model 


281  (32) 

Lognormal property of stock prices 


281  (2) 

The distribution of the rate of return 


283  (1) 


284  (2) 


286  (3) 

Concepts underlying the BlackScholesMerton differential equation 


289  (2) 

Derivation of the BlackScholesMerton differential equation 


291  (2) 


293  (2) 

BlackScholes pricing formulas 


295  (2) 

Cumulative normal distribution function 


297  (1) 

Warrants and executive stock options 


298  (2) 


300  (1) 


301  (12) 


304  (1) 


305  (1) 


306  (3) 


309  (1) 

Appendix: Proof of BlackScholesMerton formula 


310  (3) 

Options on stock indices, currencies, and futures 


313  (28) 

Results for a stock paying a known dividend yield 


313  (1) 


314  (2) 


316  (5) 


321  (2) 


323  (6) 

Valuation of futures options using binomial trees 


329  (2) 

The drift of futures prices in a riskneutral world 


331  (1) 

Black's model for valuing futures options 


332  (1) 

Futures options vs. spot options 


333  (8) 


334  (1) 


335  (1) 


336  (3) 


339  (2) 


341  (34) 


341  (1) 

Naked and covered positions 


342  (1) 


342  (2) 


344  (9) 


353  (2) 


355  (4) 

Relationship between delta, theta, and gamma 


359  (1) 


359  (3) 


362  (1) 


363  (1) 


364  (1) 


364  (3) 


367  (8) 


368  (1) 


369  (1) 


369  (2) 


371  (2) 

Appendix: Taylor series expansions and hedge parameters 


373  (2) 


375  (16) 

Putcall parity revisited 


375  (1) 


376  (3) 


379  (2) 

The volatility term structure and volatility surfaces 


381  (2) 


383  (1) 

When a single large jump is anticipated 


383  (8) 


385  (1) 


386  (1) 


386  (2) 


388  (1) 

Appendix: Determining implied riskneutral distributions from volatility smiles 


389  (2) 

Basic numerical procedures 


391  (44) 


391  (7) 

Using the binomial tree for options on indices, currencies, and futures contracts 


398  (3) 

Binomial model for a dividendpaying stock 


401  (5) 

Alternative procedures for constructing trees 


406  (3) 

Timedependent parameters 


409  (1) 


410  (7) 

Variance reduction procedures 


417  (2) 

Finite difference methods 


419  (16) 


430  (1) 


430  (1) 


431  (1) 


432  (3) 


435  (26) 


435  (3) 


438  (2) 


440  (2) 


442  (4) 


446  (2) 


448  (1) 


449  (1) 

Stress testing and back testing 


450  (1) 

Principal components analysis 


450  (11) 


454  (1) 


454  (1) 


455  (1) 


456  (2) 

Appendix: Cashflow mapping 


458  (3) 

Estimating volatilities and correlations 


461  (20) 


461  (2) 

The exponentially weighted moving average model 


463  (2) 


465  (1) 

Choosing between the models 


466  (1) 

Maximum likelihood methods 


467  (4) 

Using GARCH (1,1) to forecast future volatility 


471  (4) 


475  (6) 


477  (1) 


478  (1) 


478  (2) 


480  (1) 


481  (26) 


481  (1) 

Historical default probabilities 


482  (1) 


483  (1) 

Estimating default probabilities from bond prices 


484  (2) 

Comparison of default probability estimates 


486  (3) 

Using equity prices to estimate default probabilities 


489  (2) 

Credit risk in derivatives transactions 


491  (2) 


493  (2) 


495  (4) 


499  (8) 


502  (1) 


503  (1) 


503  (2) 


505  (2) 


507  (22) 


507  (3) 


510  (1) 

Valuation of credit default swaps 


510  (4) 


514  (1) 


515  (1) 

Basket credit default swaps 


516  (1) 

Collateralized debt obligations 


516  (3) 

Valuation of a basket CDS and CDO 


519  (1) 


520  (9) 


523  (1) 


524  (1) 


524  (2) 


526  (3) 


529  (22) 


529  (1) 

Nonstandard American options 


530  (1) 


531  (1) 


531  (1) 


532  (1) 


533  (2) 


535  (1) 


536  (1) 


537  (1) 


538  (2) 

Options to exchange one asset for another 


540  (1) 

Options involving several assets 


541  (1) 

Static options replication 


541  (10) 


544  (1) 


544  (1) 


545  (2) 


547  (2) 

Appendix: Calculation of moments for valuation of basket options and Asian options 


549  (2) 

Weather, energy, and insurance derivatives 


551  (10) 


551  (1) 


552  (1) 


553  (3) 


556  (5) 


557  (1) 


558  (1) 


558  (1) 


559  (2) 

More on models and numerical procedures 


561  (28) 

Alternatives to BlackScholes 


562  (4) 

Stochastic volatility models 


566  (2) 


568  (1) 

Pathdependent derivatives 


569  (4) 


573  (3) 

Options on two correlated assets 


576  (3) 

Monte Carlo simulation and American options 


579  (10) 


583  (1) 


584  (1) 


585  (1) 


586  (3) 


589  (22) 


590  (3) 


593  (1) 


594  (2) 

Alternative choices for the numeraire 


596  (3) 

Extension to several factors 


599  (1) 


600  (2) 


602  (9) 


603  (1) 


604  (1) 


604  (2) 


606  (1) 

Appendix: Handling multiple sources of uncertainty 


607  (4) 

Interest rate derivatives: the standard market models 


611  (24) 


611  (3) 


614  (5) 

Interest rate caps and floors 


619  (6) 


625  (4) 


629  (1) 

Hedging interest rate derivatives 


630  (5) 


630  (1) 


631  (1) 


631  (1) 


632  (3) 

Convexity, timing, and quanto adjustments 


635  (14) 


635  (4) 


639  (2) 


641  (8) 


644  (1) 


644  (1) 


645  (1) 


646  (2) 

Appendix: Proof of the convexity adjustment formula 


648  (1) 

Interest rate derivatives: models of the short rate 


649  (30) 


649  (1) 


650  (4) 


654  (4) 


658  (1) 


659  (1) 


660  (2) 

A general treebuilding procedure 


662  (10) 


672  (1) 

Hedging using a onefactor model 


673  (6) 


673  (1) 


674  (1) 


674  (2) 


676  (3) 

Interest rate derivatives: HJM and LMM 


679  (18) 

The Health, Jarrow, and Morton model 


679  (3) 


682  (10) 

Mortgagebacked securities 


692  (5) 


694  (1) 


695  (1) 


696  (1) 


696  (1) 


697  (16) 

Variations on the vanilla deal 


697  (2) 


699  (1) 


700  (1) 


701  (3) 


704  (1) 

Swaps with embedded options 


705  (3) 


708  (5) 


709  (1) 


710  (1) 


710  (1) 


711  (2) 


713  (16) 

Capital investment appraisal 


713  (1) 

Extension of the riskneutral valuation framework 


714  (2) 

Estimating the market price of risk 


716  (1) 

Application to the valuation of a business 


717  (1) 


717  (5) 

Evaluating options in an investment opportunity 


722  (7) 


727  (1) 


727  (1) 


727  (1) 


728  (1) 

Derivatives mishaps and what we can learn from them 


729  (12) 

Lessons for all users of derivatives 


729  (4) 

Lessons for financial institutions 


733  (4) 

Lessons for nonfinancial corporations 


737  (4) 


738  (1) 


738  (3) 
Glossary of terms 

741  (20) 
DerivaGem software 

761  (6) 
Major exchanges trading futures and options 

767  (1) 
Table for N(x) when x ≤ 0 

768  (1) 
Table for N(x) when x > 0 

769  (2) 
Author index 

771  (4) 
Subject index 

775  