Introductory Course on Financial Mathematics

Financial Instruments and Arbitrage: Time Value of Money; Forwards, Futures and Arbitrage; Bonds and Swaps; European Options; Discrete-Time Stochastic Modeling and Pricing Options: Binary Model of Price Evolution; Elements of Probability Theory; Discrete-Time Stochastic Processes; Application of Martingales and First Fundamental Theorem of Asset Pricing; Pricing and Hedging European Options on Binary Trees; Complete and Incomplete Markets; Capital Asset Pricing Model; American Options; Continuous-Time Stochastic Modelling and Black-Scholes Formula: Efficient Market Hypothesis; Probabilistic Model for Experiments with Infinitely Many Outcomes; Central Limit Theorem and Its Application; Wiener Process; Geometric Brownian Motion; Ito Integral and Stochastic Differential Equation; Ito Formula; Black-Scholes Equation; Greeks.