Course Details
Subject {L-T-P / C} : MA5331 : Mathematical Finance { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Ankur Kanaujiya
Syllabus
Fundamentals of the financial markets: Financial markets and instruments, interest rates, present and future values of cash flows, risk-free and risky assets.
Options: call option, put option, expiration date, strike price/exercise price, European, American option and exotic options, put-call parity, a basic property of options.
Binomial asset pricing model under no arbitrage condition single-period model, multiperiod model, risk-neutral probabilities, martingales in the discrete framework, risk-neutral valuation of European and American options under no arbitrage condition in the binomial framework, Introduction to continuous time models, Basic notions of probability theory on an infinite sample space, Change of measure and the Radon-Nikodym derivative, Random walk and Brownian motion, Ito integral and Ito formula Black Scholes formula for pricing a European call option.
Mean-Variance Portfolio Theory: Markowitz Model of Portfolio Optimization, Single period and multi- period mode and Capital Asset Pricing Model (CAPM).
Course Objectives
- The basic securities, organization of financial markets, the concept of interest rates, present and future value of cashflow.
- Basic property of option, no arbitrage principle, short selling, put-call parity.
- Concept of option pricing using single and multi-Period Binomial pricing models <br />and the limiting case of Cox-Ross-Rubinstein (CRR) Model as a famous Black Scholes Formula for Option Pricing.
- The portfolio construction at the overall plan level, taking into account investor <br />objectives and the practical challenges of implementation.
Course Outcomes
1. Describe and explain the fundamental features of a financial instruments. <br />2. Acquire knowledge of how options work, how they are used and how they are priced. <br />3. Evaluate the price of option using Binomial model. <br />4. Demonstrate a clear understanding of financial research planning, methodology and implementation.
Essential Reading
- H. D. Junghenn, Option valuation: A first course in financial mathematics, Chapman and Hall/CRC Financial mathematics series, 2011
- J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice-Hall of India 2007
Supplementary Reading
- M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, 2nd Ed., Springer, 2010
- S. M. Ross, An elementary introduction to mathematical finance, 3rd Ed. Cambridge University Press, 2011