The theory of pricing and hedging of derivative securities is mathematically sophisticated. This book is an introduction to the use of advanced probability theory in financial economics, presenting the necessary mathematics in a precise and rigorous manner. Professor Nielsen concentrates on three main areas: the theory of continuous-time stochastic processes, a notorious barrier to the understanding of probability theory in finance; the general theory of trading,
pricing, and hedging in continuous time, using the martingale approach; and a detailed look at the BlackScholes and the Gaussian one-factor models of the term structure of interest rates. His book enables the reader to read the journal literature with confidence, apply the methods to new problems, or
to do original research in the field.
`it is clear that Lars Nielsen has both communicated the material and excited his students with his approach.'
Bruce D. Grundy, The Jnl of Financial Research Vol.XXIII, No.3. Fall 2000.
`This is a challenging and rewarding text. It will lead mathematics graduate students toward an interest in the problems of finance. It will lead finance graduate students toward the level of mathematical sophistication neccessary to contribute to the literature in this field. It will also allow some academics currently teaching undergraduate and MBA derivatives courses to confirm or challenge their own often intuitive understanding of pricing, hedging
Bruce D. Grundy, The Jnl of Financial Research. Vol.XXIII, No.3. Fall 2000.
"this book will prove valuable for those teaching graduate courses in continuous time finance and for researchers and practitioners who require access to a good reference book." Economic Journal
1: Stochastic Processes
2: Ito Calculus
3: Gaussian Processes
4: Securities and Trading Strategies
5: The Martingale Valuation Principle
6: The Black-Scholes Model
7: Gaussian Term Structure Models
Appendix A Measure and Probability
Appendix B Lebesgue Integrals and Expectations
Appendix C The Heat Equation
Appendix D Suggested Solutions to Exercises for Chapters 1-7
Appendix E Suggested Solutions to Exercises for Appendix A and B