id,title,slug,link,category_id,tags,type_id,image,provider_id,publisher_id,university_id,institution_id,duration,cost_id,certificate,difficulty,description,syllabus,pages,added_date,published_date,bad_link,popular
84006,"Mathematical Finance",mathematical-finance-84006,https://study.com/academy/course/west-mathematics-practice-study-guide.html?adkey=81b99b454dbf432fa8cb8ad2c69ac333,10,55,1,https://ccweb.imgix.net/https%3A%2F%2Fimg.youtube.com%2Fvi%2FIrWeySxY9OA%2Fhqdefault.jpg?ar=16%3A9&auto=format&cs=strip&fit=crop&h=380&ixlib=php-4.1.0&w=535&s=ee8c3bf520b6640b3330f5f89cbc7cba,7,,1449,20,,,,,"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 theoryINDUSTRY SUPPORT: Finance Industry","
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 expectationWeek 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.