Research Catalog
Stochastic processes with applications to finance
- Title
- Stochastic processes with applications to finance / Masaaki Kijima.
- Author
- Publication
- Boca Raton, Fla. : Chapman & Hall/CRC, ©2003.
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1 Item
| Status | Format | Access | Call Number | Item Location |
|---|---|---|---|---|
| Text | Use in library | QA274 .K554 2003 | Off-site |
Details
- Description
- xi, 274 pages : illustrations; 24 cm
- Subject
- Bibliography (note)
- Includes bibliographical references (p. 261-264) and index.
- Contents
- 1 Elementary Calculus: Towards Ito's Formula 1 -- 1.1 Exponential and Logarithmic Functions 1 -- 1.2 Differentiation 4 -- 1.3 Taylor's Expansion 8 -- 1.4 Ito's Formula 10 -- 1.5 Integration 11 -- 2 Elements in Probability 19 -- 2.1 The Sample Space and Probability 19 -- 2.2 Discrete Random Variables 21 -- 2.3 Continuous Random Variables 23 -- 2.4 Multivariate Random Variables 25 -- 2.5 Expectation 28 -- 2.6 Conditional Expectation 32 -- 2.7 Moment Generating Functions 35 -- 3 Useful Distributions in Finance 41 -- 3.1 Binomial Distributions 41 -- 3.2 Other Discrete Distributions 43 -- 3.3 Normal and Log-Normal Distributions 46 -- 3.4 Other Continuous Distributions 50 -- 3.5 Multivariate Normal Distributions 53 -- 4 Derivative Securities 61 -- 4.1 The Money-Market Account 61 -- 4.2 Various Interest Rates 62 -- 4.3 Forward and Futures Contracts 66 -- 4.4 Options 68 -- 4.5 Interest-Rate Derivatives 70 -- 5 A Discrete-Time Model for Securities Market 75 -- 5.1 Price Processes 75 -- 5.2 The Portfolio Value and Stochastic Integral 78 -- 5.3 No-Arbitrage and Replicating Portfolios 80 -- 5.4 Martingales and the Asset Pricing Theorem 84 -- 5.5 American Options 88 -- 5.6 Change of Measure 90 -- 6 Random Walks 95 -- 6.1 The Mathematical Definition 95 -- 6.2 Transition Probabilities 96 -- 6.3 The Reflection Principle 99 -- 6.4 The Change of Measure Revisited 102 -- 6.5 The Binomial Securities Market Model 105 -- 7 The Binomial Model 111 -- 7.1 The Single-Period Model 111 -- 7.2 The Multi-Period Model 114 -- 7.3 The Binomial Model for American Options 118 -- 7.4 The Trinomial Model 119 -- 7.5 The Binomial Model for Interest-Rate Claims 121 -- 8 A Discrete-Time Model for Defaultable Securities 127 -- 8.1 The Hazard Rate 127 -- 8.2 A Discrete Hazard Model 129 -- 8.3 Pricing of Defaultable Securities 131 -- 8.4 Correlated Defaults 135 -- 9 Markov Chains 141 -- 9.1 Markov and Strong Markov Properties 141 -- 9.2 Transition Probabilities 142 -- 9.3 Absorbing Markov Chains 145 -- 9.4 Applications to Finance 148 -- 10 Monte Carlo Simulation 157 -- 10.1 Mathematical Backgrounds 157 -- 10.2 The Idea of Monte Carlo 159 -- 10.3 Generation of Random Numbers 162 -- 10.4 Some Examples from Financial Engineering 165 -- 10.5 Variance Reduction Methods 169 -- 11 From Discrete to Continuous: Towards the Black-Scholes 175 -- 11.1 Brownian Motions 175 -- 11.2 The Central Limit Theorem Revisited 178 -- 11.3 The Black-Scholes Formula 181 -- 11.4 More on Brownian Motions 183 -- 11.5 Poisson Processes 187 -- 12 Basic Stochastic Processes in Continuous Time 193 -- 12.1 Diffusion Processes 193 -- 12.2 Sample Paths of Brownian Motions 197 -- 12.3 Martingales 199 -- 12.4 Stochastic Integrals 202 -- 12.5 Stochastic Differential Equations 205 -- 12.6 Ito's Formula Revisited 208 -- 13 A Continuous-Time Model for Securities Market 215 -- 13.1 Self-Financing Portfolio and No-Arbitrage 215 -- 13.2 Price Process Models 217 -- 13.3 The Black-Scholes Model 222 -- 13.4 The Risk-Neutral Method 225 -- 13.5 The Forward-Neutral Method 231 -- 13.6 The Interest-Rate Term Structure 234 -- 13.7 Pricing of Interest-Rate Derivatives 241 -- 13.8 Pricing of Corporate Debts 245.
- ISBN
- 1584882247
- 9781584882244
- LCCN
- 2002067482
- 9781584882244
- OCLC
- ocm49679440
- 49679440
- SCSB-9184933
- Owning Institutions
- Princeton University Library