Computational analysis of dynamic behavior of the ornstein-uhlenbeck process and its applications in financial engineering

《ornstein-uhlenbeck 过程动态指标的计算分析及其在金融工程中的运用(英文版)》

notation

chapter 0 introduction and summary

0.1 convergence of the ehrenfest process to the o-u process

0.2 probability generating function of the ehrenfest process

0.3 first passage time structure of the ehrenfest process

0.4 uniformization procedure of keilson

0.5 dynamic behavior of modified o-u processes with various boundaries

0.6 applications of o-u processes in financial engineering

chapter 1 first passage time structure of the ehrenfest process

1.1 spectra] representation of transition probability matrix of the ehrenfest process

1.1.1 definition of the ehrenfest process

1.1.2 probability generating functions of transition probabilities of the ehrenfest process

1.1.3 spectral representation of the ehrenfest process

1.2 first passage times and the historical maximum of the ehrenfest process

1.2.1 definition of the first passage time and historical maximum

1.2.2 first passage time structure of a general birth-death process

1.2.3 first passage time structure of the ehrenfest process

chapter 2 convergence in law of the ehrenfest process to the ornstein-uhlenbeck process

2.1 convergence of a sequence of ehreufest processes to

.the o-u process

2.1.1 definition of the o-o process

2.1.2 convergence of transition probabilities

2.1.3 convergence of first passage times and historical maximum

2.2 development of algorithms and numerical results

2.2.1 transition probabilities and tail probabilities

2.2.2 first passage times and the historical maximum

chapter 3 dynamic behavior of modified ornstein-uhlenbeck processes with various boundaries

3.1 keilson's uniformization procedure

3.1.1 uniformization procedure

3.1.2 transition probabilities of a general birth-death process

3.2 first passage times and historical maximums for o-u processes with absorbing boundaries

3.2.1 first passage times and historical maximums of markov chains

3.2.2 o-u processes with absorbing boundaries

3.3 tail probabilities of o-u processes with replacement and reflection boundaries

3.3.1 o-u processes with two replacement boundaries

3.3.2 o-u processes with two reflection boundaries

3.4 numcerical results

3.4.1 o-u processes with one absorbing boundary

3.4.2 o-u processes with two absorbing boundaries

3.4.3 o-u processes with two replacement and reflection boundaries

chapter 4 applications of ornstein-uhlenbeek processes in financial engineering

4.1 the o-u process in the hull-white model and the proposed approach

4.1.1 the vasicek model and associated shift function

4.1.2 the hun-white model with stepwise reversion and volatility functions

4.2 modification of the hull-white trinomial tree approach

4.2.1 the original hull-white trinomial tree approach

4.2.2 modified trinomial tree approach

4.3 development of computational procedures for evaluating

prices of discount bonds and european options for the vasicek model

4.3.i discount bond and european option pricing with constant reversion and volatility functions

4.3.2 numerical comparison and accuracy check

4.4 pricing discount bonds and associated european options with stepwise reversion and volatility functions

4.4.1 discount bond pricing with stepwise reversion and volatility functions

4.4.2 european option pricing with stepwise reversion and volatility functions

4.4.3 numerical results

chapter 5 concluding remarks

appendix a laguerre transform

a.1laguerre functions and laguerre coefficients

a.2 extended laguerre functions

a.3 accuracy and utility

a.4 application for normal distribution

bibliography