Ese libro es una introducción a la teoría de valuación y cobertura de activos derivados en tiempo continuo, destinado a estudiantes universitarios avanzados e investigadores en la industria financiera. Lars Tyge Nielsen es responsible de gerenciameiento de modelos de riesgo en Morgan Stanley Dean Witter & Co en Nueva York. Ha obtenido su doctorado en Harvard y es presidente de la Asociación Europea de Finanzas. También es profesor titular en el Insead, y como director asociado, ha dirigido el programa doctoral de dicha institución.

Nuestra calificación: *****

Dificultad matemática: ****

Capítulos:

1.1 Basic Notions

1.2 Brownian Motions

1.3 Generalized Brownian Motions

1.4 Information Structures

1.5 Wiener Processes

1.6 Generalized Wiener Processes

1.7 Identification of Processes

1.8 Time Integrals

1.9 Stochastic Integrals

1.10 Predictable Processes

1.11 Summary

1.12 Notes

2.1 Ito Processes and Ito's Lemma

2.2 Integrals with Respect to Ito Processes

2.3 Further Manipulations of lto's Formula

2.4 Stochastic Exponentials

2.5 Girsanov's Theorem

2.6 Summary

2.7 Notes

Gaussian Processes

3.1 Basic Notions

3.2 Deterministic Integrands

3.3 Brownian Bridge Processes

3.4 Conditionally Gaussian One-factor Processece

3.5 Ornstein-Uhlenbeck Processes

3.6 Summary

3.7 Notes

4.1 Elements of the Model

4.2 Almost Simple Trading Strategies

4.3 State Prices

4.4 The Interest Rate and the Prices of Risk

4.5 Existence and 'Uniqueness of Prices of Risk

4.6 Arbitrage and Admissibility

4.7 The Doubling Strategy

4.8 Changing the Unit of Account

4.9 Summary

4.10 Notes

5.1 Replication of Claims

5.2 Delta Hedging

5.3 Making a Trading Strategy Self-financing

5.4 Dynamically Complete Markets

5.5 How to Replicate

5.6 Example: Cash-or-nothing Options

5.7 The State Price Process as a Primitive

5.8 Risk-adjusted Probabilities

5.9 Summary

5.10 Notes

6.1 Review of the Black-Scholes Economy

6.2 The Value Function

6.3 Cash-or-nothing Options Revisited

6.4 Asset-or-nothing Options

6.5 Standard Call Options

6.6 Standard Put Options

6.7 Black-Scholes and the Heat Equation

6.8 The Black-Scholes PDE: Terminal Data

6.9 The Black-Scholes PDE: Integrability

6.10 The Black-Scholes PDE: Uniqueness

6.11 Summary

6.12 Notes

7.1 Zero-coupon Bonds and Forward Rates

7.2 The Vasicek Model

7.3 The Risk-adjusted Dynamics as Primitives

7.4 The Vasicek Model: Forward Rates

7.5 The Vasicek Model: Yields

7.6 The Merton Model

7.7 The Extended Vasicek Model

7.8 The Simplified Hull-White Model

7.9 The Continuous-time Ho-Lee Model

7.10 Summary

7.11 Notes

A Measure and Probability

A.1 Sigma-algebras

A,2 Measures and Measure Spaces

A.3 Borel Sigma-algebras and Lebesgue Measures

A.4 Measurable Mappings

A.5 Convergence in Probability

A.6 Measures and Distribution Functions

A.7 Stochastic Independence

B Lebesgue Integrals and Expectations

B.1 Lebesgue Integration

B.2 Tonelli's and Fubini's Theorems

B.3 Densities and Absolute Continuity

B.4 Locally Integrable Functions

B.5 Conditional Expectations and Probabilities

B.6 LP-spaces