Models for Financial Economics

One-period binomial model on a non-dividend-paying stock, principle of no-arbitrage, risk-neutral pricing formula, one-period binomial model on stocks, stock paying dividends continuously at a rate proportional to its price, currency, and futures contract, Multi-period setting for pricing European and American options, binomial model from market stock price data, Forward binomial tree, Cox-Ross-Rubinstein tree, lognormal tree. Black-Scholes model: lognormal distribution, probabilities and percentiles, means and variances, conditional expectations, analytic pricing formulas: cash-or-nothing calls and puts, asset-or-nothing calls and puts, ordinary calls and puts (the Black-Scholes formula), gap calls and puts, risk-neutral pricing formula using Monte-Carlo simulation, inverse transformation, path-independent and path-dependent options, Antithetic variate, stratified sampling, control variate, Black-Scholes formula to price exchange options, rate of appreciation, historical volatility, implied volatility, Option Greeks (Delta, Gamma, Theta, Vega, Rho, and Psi), Option elasticity, Sharpe ratio and instantaneous risk premium for both an option and a portfolio of options and the underlying stock, Black-Derman-Toy tree, interest rate caplets, floorlets and bond calls and puts.