Course Description
Bonds, stock markets, derivatives, arbitrage, and binomial tree models for stocks and options, Black-Scholes formula for options pricing, hedging. Computational methods will be incorporated.
Additional Requirements for Graduate Students:
Graduate students will be asked to submit additional, more
extensive homework problems requiring deeper synthesis of the
concepts and material. Graduate students' term projects will
also be expected to be more extensive, reviewing and integrating
the materials more thoroughly, and will be graded at a higher
standard than the undergraduate projects.
Athena Title
Mathematics of Option Pricing
Prerequisite
[(MATH 2270 or MATH 2500) and MATH 3000] or [(MATH 2270 or MATH 2500) and MATH 3200 and MATH 3300] or MATH 3510 or MATH 3510H or permission of department
Grading System
A - F (Traditional)
Course Objectives
A familiarity with the derivative financial instrument known as an option, and a basic understanding of the mathematical inputs to the formulas and models used for the pricing of such options. Experience with the use of Excel and Maple, in conjunction with real-life data, to estimate parameters of the formulas and models, and to draw financial inferences from the formulas and models.
Topical Outline
1.Basic financial instruments and strategies: stocks, bonds, options, short-selling. Discrete and continuous rates of interest, exponential and logarithm functions, present value calculations. 2. The binomial tree model for pricing stocks and options. Elementary probability theory, expected value, binomial coefficients, matrix theory. Arbitrage, risk neutral probabilites, hedge portfolios and replicating portfolios. 3. Using Excel, Maple and real-life data to estimate the parameters of the binomial tree model, and to compute stock and option tree prices. Variance and standard deviation. 4. Random walks, limits of random walks, computer simulations, Brownian paths. 5. Normal distributions and the statement of the Central Limit Theorem. 6. Integrals and antiderivatives, modelling by differential equations, and the continuous model for stock prices. 7. The Black-Scholes formula, using risk-free interest rates. 8. Using Excel, Maple and real-life data to estimate model parameters and option prices. 9. The Black-Scholes formula using partial differential equations. 10. Hedging, and "the Greeks". 11. Taylor polynomial approximations, and Ito's theorem.
Syllabus