Stochastic Calculus for Finance II: ContinuousTime Models, Volume 11 (Google eBook)Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has 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 refine through classroom experience with this material are provided. 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. This book is being published in two volumes. This second volume develops stochastic calculus, martingales, riskneutral pricing, exotic options and term structure models, all in continuous time. Masters level students and researchers in mathematical finance and financial engineering will find this book useful. Steven E. Shreve is CoFounder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education. 
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Review: Stochastic Calculus Models for Finance II: Continuous Time Models (Springer Finance)
User Review  Austin  GoodreadsThis is the best, most readable book on this topic (though make no mistake, it is still a graduate level mathematics text). The .pdf of Shreve's lecture notes that eventually became this book have had a loyal following on the net for years. This should be on every quant's shelf. Read full review
Review: Stochastic Calculus Models for Finance II: Continuous Time Models (Springer Finance)
User Review  Joe Malicki  GoodreadsIf I'm going to learn stochastic calculus this rigorously, I want more indepth treatment of Ito's lemma and the like to know how much to believe it and what the proofs really depend on. If you're not ... Read full review
Contents
1  
7  
13 Expectations  13 
14 Convergence of Integrals  23 
15 Computation of Expectations  27 
16 Change of Measure  32 
17 Summary  39 
18 Notes  41 
73 Knockout Barrier Options  299 
731 UpandOut Call  300 
733 Computation of the Price of the UpandOut Call  304 
74 Lookback Options  308 
742 BlackScholesMerton Equation  309 
743 Reduction of Dimension  312 
744 Computation of the Price of the Lookback Option  314 
75 Asian Options  320 
Information and Conditioning  49 
22 Independence  53 
23 General Conditional Expectations  66 
24 Summary  75 
25 Notes  77 
Brownian Motion  83 
322 Increments of the Symmetric Random Walk  84 
323 Martingale Property for the Symmetric Random Walk  85 
325 Scaled Symmetric Random Walk  86 
326 Limiting Distribution of the Scaled Random Walk  88 
327 LogNormal Distribution as the Limit of the Binomial Model  91 
332 Distribution of Brownian Motion  95 
333 Filtration for Brownian Motion  97 
334 Martingale Property for Brownian Motion  98 
341 FirstOrder Variation  99 
342 Quadratic Variation  101 
343 Volatility of Geometric Brownian Motion  106 
35 Markov Property  107 
36 First Passage Time Distribution  108 
37 Reflection Principle  111 
372 First Passage Time Distribution  112 
373 Distribution of Brownian Motion and Its Maximum  113 
38 Summary  115 
39 Notes  116 
310 Exercises  117 
Stochastic Calculus  125 
421 Construction of the Integral  126 
422 Properties of the Integral  128 
43 Itos Integral for General Integrands  132 
44 ItoDoeblin Formula  137 
442 Formula for Ito Processes  143 
443 Examples  147 
45 BlackScholesMerton Equation  153 
451 Evolution of Portfolio Value  154 
452 Evolution of Option Value  155 
453 Equating the Evolutions  156 
454 Solution to the BlackScholesMerton Equation  158 
455 The Greeks  159 
456 PutCall Parity  162 
462 ItoDoeblin Formula for Multiple Processes  165 
463 Recognizing a Brownian Motion  168 
47 Brownian Bridge  172 
472 Brownian Bridge as a Gaussian Process  175 
473 Brownian Bridge as a Scaled Stochastic Integral  176 
474 Multidimensional Distribution of the Brownian Bridge  178 
475 Brownian Bridge as a Conditioned Brownian Motion  182 
48 Summary  183 
49 Notes  187 
410 Exercises  189 
RiskNeutral Pricing  209 
522 Stock Under the RiskNeutral Measure  214 
523 Value of Portfolio Process Under the RiskNeutral Measure  217 
524 Pricing Under the RiskNeutral Measure  218 
53 Martingale Representation Theorem  221 
532 Hedging with One Stock  222 
54 Fundamental Theorems of Asset Pricing  224 
542 Multidimensional Market Model  226 
543 Existence of the RiskNeutral Measure  228 
544 Uniqueness of the RiskNeutral Measure  231 
55 DividendPay ing Stocks  234 
551 Continuously Paying Dividend  235 
552 Continuously Paying Dividend with Constant Coefficients  237 
553 Lump Payments of Dividends  238 
554 Lump Payments of Dividends with Constant Coefficients  239 
56 Forwards and Futures  240 
562 Futures Contracts  241 
563 ForwardFutures Spread  247 
57 Summary  248 
58 Notes  250 
59 Exercises  251 
Connections with Partial Differential Equations  263 
63 The Markov Property  266 
64 Partial Differential Equations  268 
65 Interest Rate Models  272 
66 Multidimensional FeynmanKac Theorems  277 
67 Summary  280 
68 Notes  281 
69 Exercises  282 
Exotic Options  295 
752 Augmentation of the State  321 
753 Change of Numeraire  323 
76 Summary  331 
78 Exercises  332 
American Derivative Securities  339 
82 Stopping Times  340 
83 Perpetual American Put  345 
831 Price Under Arbitrary Exercise  346 
832 Price Under Optimal Exercise  349 
833 Analytical Characterization of the Put Price  351 
834 Probabilistic Characterization of the Put Price  353 
84 FiniteExpiration American Put  356 
841 Analytical Characterization of the Put Price  357 
842 Probabilistic Characterization of the Put Price  359 
85 American Call  361 
852 Underlying Asset Pays Dividends  363 
86 Summary  368 
87 Notes  369 
88 Exercises  370 
Change of Numeraire  375 
92 Numeraire  376 
93 Foreign and Domestic RiskNeutral Measures  381 
932 Domestic RiskNeutral Measure  383 
933 Foreign RiskNeutral Measure  385 
934 Siegels Exchange Rate Paradox  387 
935 Forward Exchange Rates  388 
936 GarmanKohlhagen Formula  390 
94 Forward Measures  392 
943 Option Pricing with a Random Interest Rate  394 
95 Summary  397 
96 Notes  398 
10 TermStructure Models  403 
102 AffineYield Models  405 
1021 TwoFactor Vasicek Model  406 
1022 TwoFactor CIR Model  420 
1023 Mixed Model  422 
103 HeathJarrowMorton Model  423 
1032 Dynamics of Forward Rates and Bond Prices  425 
1033 NoArbitrage Condition  426 
1034 HJM Under RiskNeutral Measure  429 
1035 Relation to AffineYield Models  430 
1036 Implementation of HJM  432 
104 Forward LIBOR Model  435 
1042 LIBOR and Forward LIBOR  436 
1043 Pricing a Backset LIBOR Contract  437 
1044 Black Caplet Formula  438 
1045 Forward LIBOR and ZeroCoupon Bond Volatilities  440 
1046 A Forward LIBOR TermStructure Model  442 
105 Summary  447 
106 Notes  450 
107 Exercises  451 
Introduction to Jump Processes  461 
112 Poisson Process  462 
1122 Construction of a Poisson Process  463 
1124 Mean and Variance of Poisson Increments  466 
1125 Martingale Property  467 
113 Compound Poisson Process  468 
1132 MomentGenerating Function  470 
114 Jump Processes and Their Integrals  473 
1141 Jump Processes  474 
1142 Quadratic Variation  479 
115 Stochastic Calculus for Jump Processes  483 
1152 ItoDoeblin Formula for Multiple Jump Processes  489 
116 Change of Measure  492 
1161 Change of Measure for a Poisson Process  493 
1162 Change of Measure for a Compound Poisson Process  495 
1163 Change of Measure for a Compound Poisson Process and a Brownian Motion  502 
117 Pricing a European Call in a Jump Model  505 
1172 Asset Driven by a Brownian Motion and a Compound Poisson Process  512 
118 Summary  523 
119 Notes  525 
Advanced Topics in Probability Theory  527 
A2 Generating cralgebras  530 
A3 Random Variable with Neither Density nor Probability Mass Function  531 
B Existence of Conditional Expectations  533 
C Completion of the Proof of the Second Fundamental Theorem of Asset Pricing  535 
537  
545  
Common terms and phrases
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References to this book
The Mathematics of Arbitrage, Volume 13 Freddy Delbaen,Walter Schachermayer No preview available  2006 
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Math 503 Spring 2006 Syllabus
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