MAL 732 (Financial Mathematics)
(
Course
Contents:
1. Some Basic Definitions and Terminology.
2. Basic Theory of Option Pricing: Single and Multi-Period Binomial Pricing Models, Cox-Ross-Rubinstein (CRR) Model, Black-Scholes Formula for Option Pricing as a Limit of CRR Model.
3.
Brownian and Geometric Brownian
Motion, Theory of Martingales. Stochastic Calculus,
Stochastic Differential Equations, Ito’s Formula to Solve SDE’s. Applications
of Stochastic Calculus in Option Pricing.
4.
Mean-Variance Portfolio Theory:
Markowitz Model of Portfolio Optimization and Capital Asset Pricing Model
(CAPM). Limitations of Markowitz Model and New Measures of Risk. 5.
Interest Rates and Interest
Rate Derivatives: Binomial Lattice Model, Vasicek,
Hull and White Models for Bond Pricing. Prerequisite: Probability Theory and Stochastic Process (MAL 250/MAL 509) and
Optimization (MAL 210/MAL 526). Main
Books: 1.
D. G. Luenberger:
Investment Science, Oxford University Press, 1999. 2.
M. Capińsky
and T. Zastawniak: Mathematics for Finance: An
Introduction to Financial Engineering, Springer, 2004. 3.
Thomas Mikosch:
Elementary Stochastic Calculus with Finance in view, World Scientific, 2006. 4.
Suresh Chandra, S. Dharmaraja, Aparna Mehra, R. Khemchandani:
Financial Mathematics: An Introduction, Narosa Publishing House, 2012. Reference
Books: 1.
S. E. Shreve: Stochastic
Calculus for Finance, Vol. I
& Vol. II, Springer, 2004. 2.
Sean Dineen:
Probability Theory in Finance: A Mathematical Guide to the Black-Scholes Formula, American Mathematical Society, Indian
edition, 2011. Evaluation: Minor-I: 25 Marks, Minor-II: 25 Marks, Major: 50 Marks.
Any further information about this course
can be accessed from http://web.iitd.ac.in/~dharmar/MAL732/main.html (Suresh
Chandra)
(S. Dharmaraja)
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Tutorial Sheets
This page maintained by Dr. S. Dharmaraja mailto:dharmar@maths.iitd.ac.in and
last updated Monday, Aug. 11, 2014.