Derivatives Portfolio & Risk Fixed Income Corporate Finance Stochastic Models Guide

Guide

Derivatives pricing

01Forwards, calls and puts 02Combining positions 03Arbitrage and the forward price 04Put–call parity 05The one-step binomial model 06Risk-neutral probabilities 07Multi-step trees and backward induction 08American options and early exercise 09Delta and hedging 10Geometric Brownian motion 11The Black–Scholes formula 12The Greeks: gamma, vega, theta and rho 13Implied volatility and the volatility smile 14Stochastic volatility and the Heston model 15Static replication: Breeden–Litzenberger and Carr–Madan 16Exotic options: barriers, Asians and digitals

Portfolio & risk

01Returns and volatility 02Diversification and correlation 03The efficient frontier and the capital market line 04Risk aversion and the optimal complete portfolio 05CAPM, beta and the security market line 06Performance measures: Sharpe, Treynor, Jensen and information ratio 07Factor models and systematic risk 08Value at Risk and expected shortfall

01Bond prices and yields 02Duration and convexity 03Immunization and duration matching 04Spot rates, forward rates and the yield curve 05Bond futures and the cheapest-to-deliver 06Interest rate swaps 07Callable bonds and negative convexity 08Credit risk: default probabilities and credit spreads

Corporate finance

01Interest, compounding and discounting 02Annuities, perpetuities and loan amortization 03Net present value and internal rate of return 04The weighted average cost of capital 05Capital structure and the Modigliani–Miller theorems 06Discounted cash flow valuation 07Relative valuation with multiples 08Real options: the value of flexibility

Stochastic models

01Random walks and Brownian motion 02Probability spaces, σ-algebras and random variables 03Filtrations, adapted processes and stopping times 04Conditional expectation and martingales 05Properties of Brownian motion 06The reflection principle and first passage times 07The Brownian bridge 08The Itô integral 09Itô's lemma 10Kolmogorov equations and the Feynman–Kac formula 11Change of measure and Girsanov's theorem 12Monte Carlo option pricing 13Simulating SDEs: the Euler–Maruyama scheme 14Mean reversion: Ornstein–Uhlenbeck and Vasicek 15Jumps and the Merton jump-diffusion model

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