SOLUTIONS MANUAL Introduction. 1. Assets, Portfolios, and Arbitrage. 1.1. Portfolio Allocation and Short Selling. 1.2. Arbitrage. 1.3. Risk-Neutral Probability Measures. 1.4. Hedging of Contingent Claims. 1.5. Market Completeness. 1.6. Example: Binary Market. Exercises. 2. Discrete-Time Market Model. 2.1. Discrete-Time Compounding. 2.2. Arbitrage and Self-Financing Portfolios. 2.3. Contingent Claims. 2.4. Martingales and Conditional Expectations. 2.5. Market Completeness and Risk-Neutral Measures. 2.6. The Cox-Ross-Rubinstein (CRR) Market Model. Exercises. 3. Pricing and Hedging in Discrete Time. 3.1. Pricing Contingent Claims. 3.2. Pricing Vanilla Options in the CRR Model. 3.3. Hedging Contingent Claims. 3.4. Hedging Vanilla Options. 3.5. Hedging Exotic Options. 3.6. Convergence of the CRR Model. Exercises. 4. Brownian Motion and Stochastic Calculus. 4.1. Brownian Motion. 4.2. Three Constructions of Brownian Motion. 4.3. Wiener Stochastic Integral. 4.4. Itô Stochastic Integral. 4.5. Stochastic Calculus. Exer