Title The mathematics of finance : modeling and hedging / Victor Goodman, Joseph Stampfli

Published Australia Pacific Grove, CA : Brooks/Cole, [2001] ©2001

Table of Contents
1	Financial Markets					1
	1.1	Markets and Math				1
	1.2	Stocks and Their Derivatives				2
		1.2.1	Forward Stock Contracts			3
		1.2.2	Call Options			7
		1.2.3	Put Options			9
		1.2.4	Short Selling			11
	1.3	Pricing Futures Contracts				12
	1.4	Bond Markets				15
		1.4.1	Rates of Return			16
		1.4.2	The U.S. Bond Market			17
		1.4.3	Interest Rates and Forward Interest Rates			18
		1.4.4	Yield Curves			19
	1.5	Interest Rate Futures				20
		1.5.1	Determining the Futures Price			20
		1.5.2	Treasury Bill Futures			21
	1.6	Foreign Exchange				22
		1.6.1	Currency Hedging			22
		1.6.2	Computing Currency Futures			23
2	Binomial Trees, Replicating Portfolios, and Arbitrage					25
	2.1	Three Ways to Price a Derivative				25
	2.2	The Game Theory Method				26
		2.2.1	Eliminating Uncertainty			27
		2.2.2	Valuing the Option			27
		2.2.3	Arbitrage			27
		2.2.4	The Game Theory Method--A General Formula			28
	2.3	Replicating Portfolios				29
		2.3.1	The Context			30
		2.3.2	A Portfolio Match			30
		2.3.3	Expected Value Pricing Approach			31
		2.3.4	How to Remember the Pricing Probability			32
	2.4	The Probabilistic Approach				34
	2.5	Risk				36
	2.6	Repeated Binomial Trees and Arbitrage				39
	2.7	Appendix: Limits of the Arbitrage Method				41
3	Tree Models for Stocks and Options					44
	3.1	A Stock Model				44
		3.1.1	Recombining Trees			46
		3.1.2	Chaining and Expected Values			46
	3.2	Pricing a Call Option with the Tree Model				49
	3.3	Pricing an American Option				52
	3.4	Pricing an Exotic Option--Knockout Options				55
	3.5	Pricing an Exotic Option--Lookback Options				59
	3.6	Adjusting the Binomial Tree Model to Real-World Data				61
	3.7	Hedging and Pricing the N-Period Binomial Model				66
4	Using Spreadsheets to Compute Stock and Option Trees					71
	4.1	Some Spreadsheet Basics				71
	4.2	Computing European Option Trees				74
	4.3	Computing American Option Trees				77
	4.4	Computing a Barrier Option Tree				79
	4.5	Computing N-Step Trees				80
5	Continuous Models and the Black-Scholes Formula					81
	5.1	A Continuous-Time Stock Model				81
	5.2	The Discrete Model				82
	5.3	An Analysis of the Continuous Model				87
	5.4	The Black-Scholes Formula				90
	5.5	Derivation of the Black-Scholes Formula				92
		5.5.1	The Related Model			92
		5.5.2	The Expected Value			94
		5.5.3	Two Integrals			94
		5.5.4	Putting the Pieces Together			96
	5.6	Put-Call Parity				97
	5.7	Trees and Continuous Models				98
		5.7.1	Binomial Probabilities			98
		5.7.2	Approximation with Large Trees			100
		5.7.3	Scaling a Tree to Match a GBM Model			102
	5.8	The GBM Stock Price Model--A Cautionary Tale				103
	5.9	Appendix: Construction of a Brownian Path				106
6	The Analytic Approach to Black-Scholes					109
	6.1	Strategy for Obtaining the Differential Equation				110
	6.2	Expanding V(S, t)				110
	6.3	Expanding and Simplifying V(S[subscript t], t)				111
	6.4	Finding a Portfolio				112
	6.5	Solving the Black-Scholes Differential Equation				114
		6.5.1	Cash or Nothing Option			114
		6.5.2	Stock-or-Nothing Option			115
		6.5.3	European Call			116
	6.6	Options on Futures				116
		6.6.1	Call on a Futures Contract			117
		6.6.2	A PDE for Options on Futures			118
	6.7	Appendix: Portfolio Differentials				120
7	Hedging					122
	7.1	Delta Hedging				122
		7.1.1	Hedging, Dynamic Programming, and a Proof that Black-Scholes Really Works in an Idealized World			123
		7.1.2	Why the Foregoing Argument Does Not Hold in the Real World			124
		7.1.3	Earlier [Delta] Hedges			125
	7.2	Methods for Hedging a Stock or Portfolio				126
		7.2.1	Hedging with Puts			126
		7.2.2	Hedging with Collars			127
		7.2.3	Hedging with Paired Trades			127
		7.2.4	Correlation-Based Hedges			127
		7.2.5	Hedging in the Real World			128
	7.3	Implied Volatility				128
		7.3.1	Computing [sigma subscript 1] with Maple			128
		7.3.2	The Volatility Smile			129
	7.4	The Parameters [Delta], [Gamma], and [Theta]				130
		7.4.1	The Role of [Gamma]			131
		7.4.2	A Further Role for [Delta], [Gamma], [Theta]			133
	7.5	Derivation of the Delta Hedging Rule				134
	7.6	Delta Hedging a Stock Purchase				135
8	Bond Models and Interest Rate Options					137
	8.1	Interest Rates and Forward Rates				137
		8.1.1	Size			138
		8.1.2	The Yield Curve			138
		8.1.3	How Is the Yield Curve Determined?			139
		8.1.4	Forward Rates			139
	8.2	Zero-Coupon Bonds				140
		8.2.1	Forward Rates and ZCBs			140
		8.2.2	Computations Based on Y(t) or P(t)			142
	8.3	Swaps				144
		8.3.1	Another Variation on Payments			147
		8.3.2	A More Realistic Scenario			148
		8.3.3	Models for Bond Prices			149
		8.3.4	Arbitrage			150
	8.4	Pricing and Hedging a Swap				152
		8.4.1	Arithmetic Interest Rates			153
		8.4.2	Geometric Interest Rates			155
	8.5	Interest Rate Models				157
		8.5.1	Discrete Interest Rate Models			158
		8.5.2	Pricing ZCBs from the Interest Rate Model			162
		8.5.3	The Bond Price Paradox			165
		8.5.4	Can the Expected Value Pricing Method Be Arbitraged?			166
		8.5.5	Continuous Models			171
		8.5.6	A Bond Price Model			171
		8.5.7	A Simple Example			174
		8.5.8	The Vasicek Model			178
	8.6	Bond Price Dynamics				180
	8.7	A Bond Price Formula				181
	8.8	Bond Prices, Spot Rates, and HJM				183
		8.8.1	Example: The Hall-White Model			184
	8.9	The Derivative Approach to HJM: The HJM Miracle				186
	8.10	Appendix: Forward Rate Drift				188
9	Computational Methods for Bonds					190
	9.1	Tree Models for Bond Prices				190
		9.1.1	Fair and Unfair Games			190
		9.1.2	The Ho-Lee Model			192
	9.2	A Binomial Vasicek Model: A Mean Reversion Model				200
		9.2.1	The Base Case			201
		9.2.2	The General Induction Step			202
10	Currency Markets and Foreign Exchange Risks					207
	10.1	The Mechanics of Trading				207
	10.2	Currency Forwards: Interest Rate Parity				209
	10.3	Foreign Currency Options				211
		10.3.1	The Garman-Kohlhagen Formula			211
		10.3.2	Put-Call Parity for Currency Options			213
	10.4	Guaranteed Exchange Rates and Quantos				214
		10.4.1	The Bond Hedge			215
		10.4.2	Pricing the GER Forward on a Stock			216
		10.4.3	Pricing the GER Put or Call Option			219
	10.5	To Hedge or Not to Hedge--and How Much				220
11	International Political Risk Analysis					221
	11.1	Introduction				221
	11.2	Types of International Risks				222
		11.2.1	Political Risk			222
		11.2.2	Managing International Risk			223
		11.2.3	Diversification			223
		11.2.4	Political Risk and Export Credit Insurance			224
	11.3	Credit Derivatives and the Management of Political Risk				225
		11.3.1	Foreign Currency and Derivatives			225
		11.3.2	Credit Default Risk and Derivatives			226
	11.4	Pricing International Political Risk				228
		11.4.1	The Credit Spread or Risk Premium on Bonds			229
	11.5	Two Models for Determining the Risk Premium				230
		11.5.1	The Black-Scholes Approach to Pricing Risky Debt			230
		11.5.2	An Alternative Approach to Pricing Risky Debt			234
	11.6	A Hypothetical Example of the JLT Model				238
	Answers to Selected Exercises					241
	Index					247

Copies

Location	Call no.	Vol.	Availability
MELB	332.0414 Goo/Mof		AVAILABLE

Description xiv, 250 pages ; 24 cm Series The Brooks/Cole series in advanced mathematics Brooks/Cole series in advanced mathematics. Notes Includes index Subject Capital market -- Mathematical models. Hedging (Finance) Author Stampfli, Joseph G. (Joseph Gail), 1932- LC no. 00057205 ISBN 0534377769 casebound

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