Derivative Securities

DERIVATIVE SECURITIES
by Robert A. Jarrow and Stuart M. Turnbull
South-Western College Publishing(2^nd Edition)
From the Book Website (http://jarrow.swcollege.com) The risk of losing your students in the complex maze of derivative securities issues can be great. *Derivative Securities, 2e* by Robert Jarrow and Stuart Turnbull takes the risk out of your classroom by making the theory and practice of pricing and hedging derivative securities accessible to students in a simple and complete manner. Written by two of the foremost experts in the industry, Derivative Securities, 2e includes crucial coverage of option pricing, futures pricing, equity, index, foreign currency, commodity, and interest rate derivatives as well as exotic options. This is without the watering down of material commonly found in other texts. Building on the success of their first edition,Jarrow and Turnbull include more applied theory, updated regulatory issues, and developments in credit risk to reflect the latest issues in the derivative securities field.
Table of Contents
Note: The chapters that are marked with * are recommended for the entrance examination.
Preface			xvii

PART 1 THE BASICS
*1 INTRODUCTION TO DERIVATIVES SECURITIES			2
	1.0	Introduction	2
	1.1	Forward Contracts	3
		Formalization	4
	1.2	Futures Contracts	6
		Strandardization	6
		Clearing House	8
		Settlement Price	9
		Daily Settlement and Margins	10
		Regulation	11
		Why Standardization? Why Daily Settlement?	11
		Basis	12
		Newspaper Quotes	13
	1.3	Options	15
		Call Options	15
		Put Options	17
		American versus European Options	19
	1.4	Organized Option Markets	20
	1.5	Option Newspaper Quotes	22
	1.6	Interest Rates and Bond Prices	23
		Zero-Coupon Bond Prices	23
		Discount Rates	24
		Simple Interest Rates	25
		Discretely Compounded Interest Rates	26
		Continously Compounded Interest Rates	29
	1.7	Summary	30

* 2 SIMPLE ARBITRAGE RELATIONSHIPS FOR FORWARD AND FUTURES CONTRACTS			34
	2.0	Introduction	34
	2.1	Definition of Arbitrage	34
	2.2	Assumptions	35
	2.3	Forward and Spot Prices	37
		No Cash Flows on the Underlying Asset Over the Life of the Forward Contract	37
		Formal Derivation(Cash-and-Carry)	39
		Value of a Forward Contract	41
	2.4	Known Cash Flows to the Underlying Assset	42
		Formal Derivation	44
		Value of a Forward Contract	46
	2.5	Forward Contracts on Constant Dividend Yield and Interest-Paying Assets	47
		Forward Contracts on a Stock Index	47
		Foreign Exchange Forward Contracts	48
	2.6	Forward Contracts on Commodities	51
		Storage Costs	52
		Convenience Yield	54
		The Implied Repo Rate	55
		Forward Contracts on Electricity	55
	2.7	Forward and Futures Prices Compared	56
		Equality of Forward and Futures Prices	59
		Empirical Evidence	61
	2.8	Summary	62
	Appendix: Present Value of Dividends Ove Life of Forward Contract		67

* 3 SIMPLE ARBITRAGE RELATIONSHIP FOR OPTIONS			68
	3.0	Introduction	68
	3.1	Call and Put Options	68
	3.2	Put Options	74
	3.3	Relationship Between European Call and Put Options	79
	3.4	Relationship Between Americal Call and Put Options	82
	3.5	Summary	84

PART II THE BINOMIAL MODEL
*4 ASSET PRICE DYNAMICS			90
	4.0	Introduction	90
	4.1	The Lognormal Distribution	91
	4.2	The Basic Idea(Binomial Pricing)	96
	4.3	Formal Description(Binomial Pricing)	98
	4.4	The Binomial Approximation to the Lognormal Distribution	99
	4.5	Extensions	105
	4.6	Stochastic Differential Equation Representation	105
	4.7	Complications	107
		Lognormal Distribution	107
		Continous Trading	107
		Continously Changing Prices	108
	4.8	Summary	108
	Appendix: The Expected Value of the Future Stock Price		112

* 5 THE BINOMIAL PRICING MODEL			114
	5.0	Introduction	114
	5.1	Single-Period Example	115
	5.2	Multiperiod Example	119
	5.3	The Binomial Pricing Model	123
		The Binomial Model	123
		Constructing the Synthetic Option	124
		Risk-Neutral Valuation	126
		Put Options	130
	5.4	Hedge Ratio(Delta)	133
	5.5	Lattice Parameters	133
	5.6	The Black-Scholes Option Pricing Model	137
	5.7	Forward and Futures Prices	138
		Formalization	143
	5.8	Replicating an Option on Spot with Futures	146
		Formalization	148
		Hedge Ratios	149
	5.9	Summary	150

* 6 MARTINGALE PRICING			155
	6.0	Introduction	155
	6.1	Relative Prices and Martingales	155
		The Money Market Account	156
		Risk-Neutral Valutaion	156
	6.2	Martingales and No Arbitrage	157
	6.3	Futures Prices	161
		Formal Description	165
	6.4	Summary	166
	Appendix: Proof of the Proposition		171

7 AMERICAN OPTIONS			175
	7.0	Introduction	175
	7.1	Cum-Dividend/Ex-Dividend Prices	176
	7.2	American Call Options	178
		No Dividends	178
		Dividends	181
	7.3	American Put Options	183
		Time Value	183
		Dividends	185
	7.4	Valuation	187
		American Call Options	187
		Computational Complexity	191
		American Put Options	192
	7.5	Options on Forward Contracts	195
		Call Options	196
		Put Options	198
		Valuation	199
	7.6	Summary	203

PART III THE BLACK-SCHOLES MODEL
* 8 THE BLACK-SCHOLES MODEL			210
	8.0	Introduction	210
	8.1	Continous Time Representation of Stock Price Changes	211
	8.2	Interest Rates	213
	8.3	Ito's Lemma	213
	8.4	The Equivalent Martingale Probability Distribution	215
	8.5	European Options	217
	8.6	Hedging
	8.7	Properties of the Black-Scholes Model	224
	8.8	Use of the Black-Scholes Model	227
		Historic Volatility	228
		Implied Volatility	231
	8.9	Option Strategies	233
	8.10	Partial Differential Equation	235
		Derivation	235
		Delta, Gamma and Theta	236
	8.11	Summary	237
	Appendix A		245
	Appendix B		247
	Appendix C: Unequally Spaced Observations		248
	Appendix D		249

9 EXTENSIONS TO THE BLACK-SCHOLES MODEL			251
	9.0	Introduction	251
	9.1	Known Dividend Model	251
	9.2	Pseudo-American Model	255
	9.3	The Roll Market	257
	9.4	Constant Dividend Yield Model	258
	9.5	Options on Futures and Forward Contracts	261
		Futures Contracts

Table of Contents