Stochastic Calculus for Finance I: The Binomial Asset Pricing Model (Google eBook)This book evolved from the first ten years of the Carnegie Mellon professional Masterbs program in Computational Finance. The contents of the book have been used successfully with students whose mathematics background consists of calculus and calculusbased probability. The text gives both precise statements of results, plausibility arguments, and even some proofs. But more importantly, intuitive explanations, developed and refined through classroom experience with this material, are provided throughout the book. Volume I introduces the fundamental concepts in a discretetime setting and Volume II builds on this foundation to develop stochastic calculus, martingales, riskneutral pricing, exotic options, and term structure models, all in continuous time. The book includes a selfcontained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jumpdiffusion processes. Classroomtested exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance. 
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Review: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model
User Review  Joecolelife  GoodreadsShreve's book is an excellent introduction to basic options pricing. He not only deals with plain vanilla options, but also shows how the binomial model can be used to to value exotic options. Each ... Read full review
Contents
The Binomial NoArbitrage Pricing Model  1 
12 Multiperiod Binomial Model  8 
13 Computational Considerations  15 
14 Summary  18 
15 Notes  20 
Probability Theory on Coin Toss Space  25 
22 Random Variables Distributions and Expectations  27 
23 Conditional Expectations  31 
45 American Call Options  111 
46 Summary  113 
47 Notes  115 
Random Walk  119 
52 First Passage Times  120 
53 Reflection Principle  127 
An Example  129 
55 Summary  136 
24 Martingales  36 
25 Markov Processes  44 
26 Summary  52 
27 Notes  54 
State Prices  61 
32 RadonNikodym Derivative Process  65 
33 Capital Asset Pricing Model  70 
34 Summary  80 
35 Notes  83 
American Derivative Securities  89 
42 NonPathDependent American Derivatives  90 
43 Stopping Times  96 
44 General American Derivatives  101 
56 Notes  138 
InterestRateDependent Assets  143 
62 Binomial Model for Interest Rates  144 
63 FixedIncome Derivatives  154 
64 Forward Measures  160 
65 Futures  168 
66 Summary  173 
67 Notes  174 
Proof of Fundamental Properties of Conditional Expectations  177 
181  
185  
Common terms and phrases
actual probability measure agent algorithm American derivative security arbitrage Asian option Asset Pricing binomial model caplet Chapter coin toss results compute conditional expectation Consider convex function define Definition denote derivative security price discounted stock price equation European call Example expiration Figure forward contract function vn given hedging portfolio initial stock price integer interest rate model intrinsic value investment Jensen's inequality Lemma mperiod Markov process Markov property martingale money market account noarbitrage price oneperiod optimal exercise option outcome paths payoff pays perpetual American put portfolio process portfolio value positive probability price process pricing model Problem RadonNikodym derivative random variable results in head righthand side riskneutral measure riskneutral pricing formula riskneutral probability measure satisfies sequence shares of stock short position Si(H stochastic calculus stopping strike price supermartingale symmetric random walk tail timezero price v(Sn zero zerocoupon bond
Popular passages
Page 182  Department of Mathematical Sciences, Carnegie Mellon University. 20. HEATH. D., JARROW, R., & MORTON, A. (1gg2) Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation, Econometrica 60, 77105. 21. HEATH, D., JARROW, R., & MORTON, A.
Page 181  TOY, W. (1gg0) A onefactor model of interest rates and its application to treasury bond options, Fin.