Financial Derivatives: Pricing, Applications, and Mathematics

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Cambridge University Press, Jan 12, 2004 - Business & Economics - 338 pages
Combining their corporate and academic experiences, Jamil Baz and George Chacko offer financial analysts a complete, succinct account of the principles of financial derivatives pricing. Readers with a basic knowledge of finance, calculus, probability and statistics will learn about the most powerful tools in applied finance: equity derivatives, interest rate markets, and the mathematics of pricing. Baz and Chacko apply concepts such as volatility and time, and generic pricing to the valuation of conventional and more specialized cases. Other topics include: *Interest rate markets, government and corporate bonds, swaps, caps, and swaptions *Factor models and term structure consistent models *Mathematical allocation decisions such as mean-reverting processes and jump processes *Stochastic calculus and related tools such as Kilmogorov equations, martingales techniques, stocastic control and partial differential equations Meant for financial analysts and graduate students in finance and economics, Financial Derivatives begins with basic economic principles of risk and builds up various pricing and hedging techniques from those principles. Baz and Chacko simplify the mathematical presentation, and balance theory and real analysis, making it a more accessible and practical manual. Jamil Baz holds an M.S. in Management from MIT and a Ph.D. in Business Economics from Harvard University. He is a Managing Director at Deutsche Bank in London. George Chacko has a B.S. from MIT in electrical engineering and a Ph.D. in Business Economics from Harvard University. He is an Associate Professor of Business Administration at Harvard Business School. Both authors have worked extensively for financial services firms in the private sector. They have published in leading academic journals including the Review of Financial Studies and the Journal of Financial Economics as well as practitioner journals such as the Journal of Fixed Income and the Journal of Applied Corporate Finance.
 

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Contents

Preliminary Mathematics
5
12 Another Take on Volatility and Time
8
13 A First Glance at Itos Lemma
9
Brownian Motion More on Itos Lemma
11
15 TwoDimensional Brownian Motion
14
16 Bivariate Itos Lemma
15
17 Three Paradoxes of Finance
16
The Stock FreeLunch Paradox
18
37 TermStructureConsistency Models
147
372 The HoLee Model
153
373 The HoLee Model with TimeVarying Volatility
157
374 The BlackDermanToy Model
162
38 Risky Bonds and Their Derivatives
166
381 The Merton Model
167
382 The JarrowTurnbull Model
168
39 The Heath Jarrow and Morton Approach
172

The Skill Versus Luck Paradox
19
Principles of Financial Valuation
22
22 Risk and the Equilibrium Pricing of Securities
28
23 The Binomial OptionPricing Model
41
24 Limiting OptionPricing Formula
46
25 ContinuousTime Models
47
251 The BlackScholesMerton Model Pricing Kernel Approach
48
252 The BlackScholesMerton Model Probabilistic Approach
57
253 The BlackScholesMerton Model Hedging Approach
61
26 Exotic Options
63
261 Digital Options
64
262 Power Options
65
263 Asian Options
67
264 Barrier Options
71
Interest Rate Models
78
32 Bonds and Yields
80
322 Discount Factors ZeroCoupon Rates and Coupon Bias
82
323 Forward Rates
85
33 Naive Models of Interest Rate Risk
88
332 Convexity
99
333 The Free Lunch in the Duration Model
104
34 An Overview of Interest Rate Derivatives
108
341 Bonds with Embedded Options
109
342 Forward Rate Agreements
110
343 Eurostrip Futures
112
344 The Convexity Adjustment
113
345 Swaps
118
346 Caps and Floors
120
347 Swaptions
121
35 Yield Curve Swaps
122
352 The Quanto Swap
127
36 Factor Models
131
362 The Merton Model
135
363 The Vasicek Model
139
364 The CoxIngersollRoss Model
142
365 RiskNeutral Valuation
144
310 Interest Rates as Options
180
Mathematics of Asset Pricing
184
412 Gambling Recreations
186
42 Arithmetic Brownian Motion
192
422 Moments of an Arithmetic Brownian Motion
196
423 Why Sample Paths Are Not Differentiable
198
425 Extreme Values and Hitting Times
199
426 The Arcsine Law Revisited
203
43 Geometric Brownian Motion
204
432 Moments of a Geometric Brownian Motion
207
44 Ito Calculus
209
442 Itos Lemma
214
443 Multidimensional Itos Lemma
222
45 MeanReverting Processes
225
453 Calculations of Moments with the Dynkin Operator
226
454 The SquareRoot Process
228
46 Jump Process
229
462 Time Between Two Jumps
231
463 Jump Diffusions
232
464 Itos Lemma for Jump Diffusions
233
47 Kolmogorov Equations
234
472 The Dirac Delta Function
236
48 Martingales
239
482 Some Useful Facts About Martingales
241
483 Martingales and Brownian Motion
242
49 Dynamic Programming
245
Finite Horizon
247
Infinite Horizon
248
410 Partial Differential Equations
253
4102 RiskNeutral Pricing Equation
256
4103 The Laplace Transform
257
4104 Resolution of the Kolmogorov Forward Equation
262
4105 Resolution of the RiskNeutral Pricing Equation
265
Bibliography
269
Index
327
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About the author (2004)

Jamil Baz is the chief investment strategist of GLG, a London-based hedge fund. Prior to holding this position, he was a portfolio manager with PIMCO in London, a managing director in the Proprietary Trading Group of Goldman Sachs, chief investment strategist of Deutsche Bank, and executive director of Lehman Brothers fixed income research division. Dr Baz teaches financial economics at Oxford University. He has degrees from the London School of Economics (M.Sc.), MIT (S.M.), and Harvard University (A.M., Ph.D.).

Professor George Chacko has split his time between the academic and commercial worlds during his career. His past commercial experience has included work at Accenture and Prudential Investments. Most recently, he was a managing director heading fixed income sales and trading at State Street Bank, a managing director in pension asset management at IFL, and the chief investment officer of Auda Alternative Investments. He has co-founded and sold three financial services businesses over his career. He is currently the managing partner of Confluentis Investments. His past academic experience has been at Harvard Business School, where he served as a professor in the finance department for ten years. He also served as a visiting professor at the Indian School of Business. He is currently a professor in the finance department at Santa Clara University. His research interests have been in the areas of fixed income and derivatives research, portfolio choice and construction, and the microstructure of financial markets. He has a BS from MIT in Electrical Engineering, an MBA from the University of Chicago, and an MA and PhD from Harvard University in Business Economics.

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