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Online Course

Mathematical Finance

Indian Institute of Technology Guwahati and NPTEL via Swayam

8
Found in Mathematics, Finance

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Overview

The course on ‘Mathematical Finance’ gives an introduction to this interesting and growing area. In particular, the course will cover two Nobel-prize winning frameworks, namely portfolio theory and the option pricing theory.

INTENDED AUDIENCE: Students at advanced undergraduate and postgraduate level in Mathematics, Statistics and
allied areas as well as students of Engineering and Management interested in this field.
PREREQUISITES: Background in basics of probability theory
INDUSTRY SUPPORT: Finance Industry

Syllabus

COURSE LAYOUT

Week 1: Introduction to financial markets, financial instruments, bonds, stocks and financial derivatives.
Week 2: Time value of money, simple and compound interest rate, net present value, internal rate of return and annuities.
Week 3: Markowitz portfolio theory, risk and return, two and multi asset portfolio theory, efficient frontier.
Week 4: Capital Asset Pricing Model and portfolio performance analysis.
Week 5: No arbitrage principle, pricing of forwards and futures, properties of options.
Week 6: Derivative pricing by replication in binomial model.
Week 7: Discrete probability spaces, filtration, conditional expectation
Week 8: Discrete time martingales, Markov chain, risk-neutral pricing in binomial model for European and American derivatives.
Week 9: General probability spaces, conditional expectation, Brownian motion.
Week 10: Ito integral, Ito formula, Girsanov’s theorem, martingale representation theorem, stochastic differential equation.
Week 11: Black-Scholes-Merton (BSM) model, pricing of European derivatives in BSM framework.
Week 12: Valuation of European options in BSM model, BSM formula, BSM partial differential equation, hedging, model completeness, fundamental theorems of asset pricing.


Taught by

Prof. N. Selvaraju & Prof. Siddhartha Pratim Chakrabarty

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