Stochastic Processes in Finance II

Department: 
MATH
Course Number: 
6235
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Not regularly scheduled (QCF supported)

This is the second of a two-semester sequence that develops basic probability concepts and models for working with financial markets and derivative securities. Continuous-time parameter stochastic processes are emphasized in this course. Mathematical concepts are introduced as needed.

Prerequisites: 

MATH 2403, MATH 6759

Course Text: 

No text

Topic Outline: 
  • Background on integration and on simulation
  • Brownian Motion, and Continuous-Time Martingales and their Variation
  • The Ito Stochastic Integral and its Properties, and Ito's Change-of-Variable Formula
  • Stock Prices as Geometric Brownian Motions
  • Black-Scholes Option Pricing
  • Ito Processes and Stochastic Differential Equations
  • Continuous-Time Markov Processes and the Kolmogorov Equations
  • Additional Results on Black-Scholes Option Pricing
  • Girsanov's Theorem for Change of Measure, and Martingale Representation Theorems
  • Asset Pricing theory, Risk Neutral Measures (Equivalent Martingale Measures), and Hedging
  • Pricing Specific Exotic Options
  • Continuous-Time Optimal Stopping and Pricing American Style Options