Preface 

xix  


1  (18) 


1  (1) 


2  (1) 


2  (3) 


5  (1) 


6  (4) 


10  (4) 


14  (5) 


15  (1) 


16  (1) 


17  (2) 

Mechanics of futures markets 


19  (22) 

Trading futures contracts 


19  (1) 

Specification of the futures contract 


20  (3) 

Convergence of futures price to spot price 


23  (1) 


24  (3) 


27  (4) 


31  (1) 


31  (1) 


32  (1) 


33  (2) 


35  (1) 

Forward contracts vs. futures contracts 


36  (5) 


37  (1) 

Suggestions for further reading 


38  (1) 


38  (2) 


40  (1) 

Determination of forward and futures prices 


41  (29) 

Investment assets vs. consumption assets 


41  (1) 


41  (1) 


42  (2) 


44  (1) 

Forward price for an investment asset 


45  (2) 


47  (2) 


49  (1) 

Valuing forward contracts 


49  (2) 

Are forward prices and futures prices equal? 


51  (1) 


52  (3) 

Forward and futures contracts on currencies 


55  (3) 


58  (2) 


60  (1) 


60  (1) 

Futures prices and the expected future spot price 


61  (9) 


63  (1) 

Suggestions for further reading 


64  (1) 


65  (2) 


67  (1) 

Appendix 3A: Proof that forward and futures prices are equal when interest rates are constant 


68  (2) 

Hedging strategies using futures 


70  (23) 


70  (2) 

Arguments for and against hedging 


72  (3) 


75  (3) 

Minimum variance hedge ratio 


78  (4) 


82  (4) 

Rolling the hedge forward 


86  (7) 


87  (1) 

Suggestions for further reading 


88  (1) 


88  (2) 


90  (2) 

Appendix 4A: Proof of the minimum variance hedge ratio formula 


92  (1) 


93  (32) 


93  (1) 


94  (1) 


94  (2) 


96  (2) 


98  (2) 


100  (2) 

Theories of the term structure 


102  (1) 


102  (1) 


103  (1) 


104  (6) 


110  (1) 


111  (1) 


112  (4) 

Durationbased hedging strategies 


116  (9) 


118  (1) 

Suggestions for further reading 


119  (1) 


120  (3) 


123  (2) 


125  (26) 

Mechanics of interest rate swaps 


125  (6) 

The comparativeadvantage argument 


131  (3) 

Swap quotes and LIBOR zero rates 


134  (2) 

Valuation of interest rate swaps 


136  (4) 


140  (3) 

Valuation of currency swaps 


143  (2) 


145  (6) 


146  (1) 

Suggestions for further reading 


147  (1) 


147  (2) 


149  (2) 

Mechanics of options markets 


151  (16) 


151  (1) 

Specification of stock options 


152  (3) 


155  (2) 


157  (1) 


157  (1) 


158  (2) 

The options clearing corporation 


160  (1) 


161  (1) 


161  (1) 

Warrants, executive stock options, and convertibles 


162  (1) 


163  (4) 


163  (1) 

Suggestions for further reading 


164  (1) 


164  (1) 


165  (2) 

Properties of stock options 


167  (18) 

Factors affecting option prices 


167  (3) 


170  (1) 

Upper and lower bounds for option prices 


171  (3) 


174  (1) 

Early exercise: calls on a nondividendpaying stock 


175  (2) 

Early exercise: puts on a nondividendpaying stock 


177  (1) 


178  (1) 


179  (6) 


180  (1) 

Suggestions for further reading 


181  (1) 


182  (1) 


183  (2) 

Trading strategies involving options 


185  (15) 

Strategies involving a single option and a stock 


185  (2) 


187  (7) 


194  (3) 


197  (3) 


197  (1) 

Suggestions for further reading 


198  (1) 


198  (1) 


199  (1) 

Introduction to binomial trees 


200  (16) 

A onestep binomial model 


200  (3) 


203  (2) 


205  (3) 


208  (1) 


209  (1) 


210  (1) 

Matching volatility with u and d 


211  (1) 

Binomial trees in practice 


212  (4) 


213  (1) 

Suggestions for further reading 


214  (1) 


214  (1) 


215  (1) 

A model of the behavior of stock prices 


216  (18) 


216  (1) 

Continuoustime stochastic processes 


217  (5) 

The process for stock prices 


222  (1) 


223  (2) 


225  (1) 


226  (1) 


227  (7) 


228  (1) 

Suggestions for further reading 


229  (1) 


229  (1) 


230  (2) 

Appendix 11A: Derivation of Ito's lemma 


232  (2) 


234  (33) 

Lognormal property of stock prices 


234  (2) 

The distribution of the rate of return 


236  (1) 


237  (1) 


238  (3) 

Concepts underlying the BlackScholesMerton differential equation 


241  (1) 

Derivation of the BlackScholesMerton differential equation 


242  (2) 


244  (2) 

BlackScholes pricing formulas 


246  (2) 

Cumulative normal distribution function 


248  (1) 

Warrants issued by a company on its own stock 


249  (1) 


250  (1) 


251  (1) 


252  (15) 


256  (1) 

Suggestions for further reading 


257  (1) 


258  (3) 


261  (1) 

Appendix 12A: Proof of BlackScholesMerton formula 


262  (3) 

Appendix 12B: Exact procedure for calculating the values of American calls on dividendpaying stocks 


265  (1) 

Appendix 12C: Calculation of cumulative probability in bivariate normal distribution 


266  (1) 

Options on stock indices, currencies, and futures 


267  (32) 

Results for a stock paying a known dividend yield 


267  (1) 


268  (2) 


270  (6) 


276  (2) 


278  (6) 

Valuation of futures options using binomial trees 


284  (2) 


286  (1) 

Black's model for valuing futures options 


287  (1) 

Futures options vs. spot options 


288  (11) 


289  (1) 

Suggestions for further reading 


290  (1) 


291  (3) 


294  (1) 

Appendix 13A: Derivation of differential equation satisfied by a derivative dependent on a stock providing a dividend yield 


295  (2) 

Appendix 13B: Derivation of differential equation satisfied by a derivative dependent on a futures price 


297  (2) 


299  (31) 


299  (1) 

Naked and covered positions 


300  (1) 


300  (2) 


302  (7) 


309  (3) 


312  (3) 

Relationship between delta, theta, and gamma 


315  (1) 


316  (2) 


318  (1) 


319  (1) 


319  (1) 


320  (3) 


323  (7) 


323  (1) 

Suggestions for further reading 


324  (2) 


326  (1) 


327  (2) 

Appendix 14A: Taylor series expansions and hedge parameters 


329  (1) 


330  (16) 

Putcall parity revisited 


330  (1) 


331  (3) 


334  (2) 

The volatility term structure and volatility surfaces 


336  (1) 


337  (1) 

When a single large jump is anticipated 


338  (1) 


339  (7) 


341  (1) 

Suggestions for further reading 


341  (2) 


343  (1) 


344  (1) 

Appendix 15A: Determining implied riskneutral distributions from volatility smiles 


345  (1) 


346  (26) 


346  (2) 


348  (2) 


350  (2) 


352  (4) 


356  (3) 


359  (1) 


359  (1) 

Stress testing and back testing 


360  (1) 

Principal components analysis 


360  (12) 


364  (1) 

Suggestions for further reading 


364  (1) 


365  (1) 


366  (2) 

Appendix 16A: Cashflow mapping 


368  (2) 

Appendix 16B: Use of the CornishFisher expansion to estimate VaR 


370  (2) 

Estimating volatilities and correlations 


372  (20) 


372  (2) 

The exponentially weighted moving average model 


374  (2) 


376  (1) 

Choosing between the models 


377  (1) 

Maximum likelihood methods 


378  (4) 

Using GARCH(1,1) to forecast future volatility 


382  (3) 


385  (7) 


388  (1) 

Suggestions for further reading 


388  (1) 


389  (2) 


391  (1) 


392  (43) 


392  (7) 

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


399  (3) 

Binomial model for a dividendpaying stock 


402  (3) 

Extensions to the basic tree approach 


405  (1) 

Alternative procedures for constructing trees 


406  (4) 


410  (4) 

Variance reduction procedures 


414  (4) 

Finite difference methods 


418  (9) 

Analytic approximation to American option prices 


427  (8) 


427  (1) 

Suggestions for further reading 


428  (2) 


430  (2) 


432  (1) 

Appendix 18A: Analytic approximation to American option prices of MacMillan and of BaroneAdesi and Whaley 


433  (2) 


435  (21) 


435  (1) 

Nonstandard American options 


436  (1) 


437  (1) 


437  (1) 


438  (1) 


439  (2) 


441  (1) 


441  (2) 


443  (1) 


443  (2) 

Options to exchange one asset for another 


445  (1) 


446  (1) 


447  (1) 

Static options replication 


447  (9) 


449  (1) 

Suggestions for further reading 


449  (2) 


451  (1) 


452  (2) 

Appendix 19A: Calculation of the first two moments of arithmetic averages and baskets 


454  (2) 

More on models and numerical procedures 


456  (27) 


456  (1) 


457  (1) 

Stochastic volatility models 


458  (2) 


460  (1) 

Pathdependent derivatives 


461  (4) 


465  (2) 


467  (5) 

Options on two correlated assets 


472  (2) 

Monte Carlo simulation and American options 


474  (9) 


478  (1) 

Suggestions for further reading 


479  (1) 


480  (1) 


481  (2) 


483  (25) 


484  (3) 


487  (1) 


488  (1) 

Alternative choices for the numeraire 


489  (3) 

Extension to multiple independent factors 


492  (1) 


493  (2) 


495  (2) 


497  (2) 


499  (9) 


500  (1) 

Suggestions for further reading 


500  (1) 


501  (1) 


502  (2) 

Appendix 21A: Generalizations of Ito's lemma 


504  (2) 

Appendix 21B: Expected excess return when there are multiple sources of uncertainty 


506  (2) 

Interest rate derivatives: the standard market models 


508  (29) 


508  (3) 


511  (4) 


515  (5) 


520  (4) 


524  (1) 


524  (3) 


527  (2) 


529  (1) 

Hedging interest rate derivatives 


530  (7) 


531  (1) 

Suggestions for further reading 


531  (1) 


532  (2) 


534  (2) 

Appendix 22A: Proof of the convexity adjustment formula 


536  (1) 

Interest rate derivatives: models of the short rate 


537  (34) 


537  (1) 

Onefactor equilibrium models 


538  (1) 

The Rendleman and Bartter model 


538  (1) 


539  (3) 

The Cox, Ingersoll, and Ross model 


542  (1) 

Twofactor equilibrium models 


543  (1) 


543  (1) 


544  (2) 


546  (3) 

Options on couponbearing bonds 


549  (1) 


550  (2) 

A general treebuilding procedure 


552  (11) 


563  (1) 


564  (1) 

Hedging using a onefactor model 


565  (1) 

Forward rates and futures rates 


566  (5) 


566  (1) 

Suggestions for further reading 


567  (1) 


568  (2) 


570  (1) 

Interest rate derivatives: more advanced models 


571  (23) 

Twofactor models of the short rate 


571  (3) 

The Heath, Jarrow, and Morton model 


574  (3) 


577  (9) 

Mortgagebacked securities 


586  (8) 


588  (1) 

Suggestions for further reading 


589  (1) 


590  (1) 


591  (2) 

Appendix 24A: The A(t, T), σp, and θ(t) functions in the twofactor HullWhite model 


593  (1) 


594  (16) 

Variations on the vanilla deal 


594  (1) 


595  (3) 


598  (1) 


598  (3) 


601  (1) 

Swaps with embedded options 


602  (3) 


605  (1) 


605  (5) 


606  (1) 

Suggestions for further reading 


606  (1) 


607  (1) 


607  (2) 

Appendix 25A: Valuation of an equity swap between payment dates 


609  (1) 


610  (27) 

Bond prices and the probability of default 


610  (9) 


619  (1) 

Bond prices vs. historical default experience 


619  (1) 

Riskneutral vs. realworld estimates 


620  (1) 

Using equity prices to estimate default probabilities 


621  (2) 


623  (3) 


626  (1) 


627  (3) 


630  (7) 


633  (1) 

Suggestions for further reading 


633  (1) 


634  (1) 


635  (1) 

Appendix 26A: Manipulation of the matrices of credit rating changes 


636  (1) 


637  (23) 


637  (7) 


644  (1) 


645  (1) 

Collateralized debt obligations 


646  (1) 

Adjusting derivative prices for default risk 


647  (5) 


652  (8) 


655  (1) 

Suggestions for further reading 


655  (1) 


656  (2) 


658  (2) 


660  (18) 

Capital investment appraisal 


660  (1) 

Extension of the riskneutral valuation framework 


661  (4) 

Estimating the market price of risk 


665  (1) 

Application to the valuation of a new business 


666  (1) 


667  (3) 

Evaluating options in an investment opportunity 


670  (8) 


675  (1) 

Suggestions for further reading 


676  (1) 


676  (1) 


677  (1) 

Insurance, weather, and energy derivatives 


678  (8) 


678  (1) 


679  (1) 


680  (2) 


682  (4) 


683  (1) 

Suggestions for further reading 


684  (1) 


684  (1) 


685  (1) 

Derivatives mishaps and what we can learn from them 


686  (11) 

Lessons for all users of derivatives 


686  (4) 

Lessons for financial institutions 


690  (3) 

Lessons for nonfinancial corporations 


693  (4) 


694  (1) 

Suggestions for further reading 


695  (2) 
Glossary of notation 

697  (3) 
Glossary of terms 

700  (15) 
DerivaGem software 

715  (5) 
Major exchanges trading futures and options 

720  (2) 
Table for N(x) when x ≤ 0 

722  (1) 
Table for N(x) when x ≥ 0 

723  (2) 
Author index 

725  (4) 
Subject index 

729  