Cindy L Yu

Cindy L. Yu

Position
  • Professor
Dr. Yu is a professor in the Department of Statistics at Iowa State University (ISU). She received her Ph.D. in Statistics from Cornell University in 2005 before coming to ISU. Dr. Yu’s researches include financial statistics, missing data analyses, survey statistics and causal inference. She is also affiliated with the Center for Survey Statistics and Methodology (CSSM) at ISU and is part of a team of ISU statisticians and survey professionals to develop and implement statistical methods for several national surveys related to natural resources.

Contact Info

2216 Snedecor
2438 Osborn Dr.
Ames
,
IA
50011-1090

More Information

STAT 690A: Math Finance - Continuous Time Asset Pricing Models

Fall 2020


Course Description

This is a 3 credit course. This course provides an introduction to continuous-time finance for graduate students who are interested in learning classical math finance, and major in Statistics, Economics, Mathematics, or Business Finance. My goals are (i) to help students develop necessary mathematical tools to understand continuous-time finance models; (ii) to review some major results of continuous-time finance; (iii) to introduce students to some active research areas in financial statistics, including machine learning and Bayesian analyses. The topics that are planned to be covered are given below in the Course Content.

Prerequisites

Stat 641, or Stat 642, or a stochastic process course (like Stat 554). Students with equivalent background should request permission of the instructor.

Grading

The course grade will be based on 5-6 homework assignments (80%) and a final course presentation (20%) of important articles in the area.

Course Content (Tentative)

Chapter 1: Review of Stochastic Calculus

Chapter 2: The Black-Scholes Option Pricing Model  

            2.1 Dynamic hedging and the Black-Scholes PDE

            2.2 Girsanov theorem and martingale pricing

            2.3 Feynman-Kac solution

            2.4 Black-Scholes action

Chapter 3: Option Pricing with Stochastic Volatility and Jumps

            3.1 Limitations of the log-normal model

            3.2 Jump-diffusion models

            3.3 Stochastic volatility (SV) model

            3.4 Stochastic volatility and jump (SVJ) models

Chapter 4: Term Structure of Interest Rates

            4.1 Spot rates, forward rates

            4.2 Gaussian spot rate models

            4.3 Cox, Ingersoll and Ross model

Chapter 5: Dynamic Term Structure Models and Heath-Jarrow-Morton

            5.1 Affine term structure models

            5.2 Quadratic term structure models

            5.3 Heath-Jarrow-Morton models

            5.4 LIBOR market models

Chapter 6: Credit Risk Modeling: The Structural Approach

            6.1 Merton (1974)’s model

            6.2 Models with stochastic interest rates and stationary leverage ratios

Chapter 7: Financial Modeling Using Levy Processes

            7.1 Motivation

            7.2 Time-changed Levy processes

            7.3 Option pricing under Levey processes

            7.4 Some empirical evidences

Chapter 8: Machine Learning and Markov Chain Monte Carlo Methods for Asset  Pricing

            8.1 Briefly introduce some MCMC methods implemented in asset pricing

            8.2 Briefly introduce some machine learning methods implemented in asset    

                  pricing


You can download the syllabus and course content here:  Stat 690A Syllabus and Course Content (Fall 2020)