MATH 356 - Introduction to Mathematical Finance I

3 units (fi 6)(FIRST, 3-0-0)

Simple Market Model: one-step binomial model, basic notions and assumptions. Risk-Free Assets: simple interest, zero-coupon bonds, money market account. Risky Assets: dynamic of stock prices, binomial tree model, trinomial tree model. Discrete time market model: stock and money market model, extended models. Portfolio management: risk, two securities, capital asset pricing model. Prerequisite: MATH 253 and one of STAT 265 or STAT 281, or consent of the Department.

MATH 415 - Mathematical Finance I

3 units (fi 6)(EITHER, 3-0-0)

Review of probability tools for discrete financial analysis; Conditional probabilities/expectations. Filtrations, adapted and predictable processes. Martingales, submartingales and supermartingales in discrete-time. Doob decomposition for supermartingales. Predictable representation. Discrete- time financial modes: Arbitrage, complete and incomplete markets. Self-financing property, value and gain processes. Valuation of contingent claims. Binomial model: Model specifications, Perfect hedging. Utility functions and consumption/ investment problems. European and American options in discrete time. Futures and forward contracts in discrete time. Transition to the continuous-time framework. Corequisite: STAT 471 or consent of the Department.

MATH 515 - Mathematical Finance I

3 units (fi 6)(EITHER, 3-0-0)

Review of probability tools for discrete financial analysis; Conditional probabilities/expectations. Filtrations, adapted and predictable processes. Martingales, submartingales and supermartingales in discrete-time. Doob decomposition for supermartingales. Predictable representation. Discrete-time financial modes: Arbitrage, complete and incomplete markets. Self-financing property, value and gain processes. Valuation of contingent claims. Binomial model: Model specifications, Perfect hedging. Utility functions and consumption/investment problems. European and American options in discrete time. Futures and forward contracts in discrete time. Transition to the continuous-time framework. Prerequisite: STAT 471 or consent of the Department. Note: This course may not be taken for credit if credit has already been obtained in MATH 415.

MATH 357 - Introduction to Mathematical Finance II

3 units (fi 6)(SECOND, 3-0-0)

Forward and futures contracts: forward and futures prices, hedging with futures. Options: put-call parity, bounds on option prices, time value of options. Option pricing: European and American options in the binomial tree model, Black-Scholes formula. Financial engineering: hedging option positions, hedging business risk. Variable interest rates: maturity-independent yields, general term structure. Stochastic interest rates: arbitrage pricing of bonds, interest rate derivative securities. Prerequisite: MATH 356 or consent of the Department.