Part I The Fundamentals of Derivative Security Pricing -- 1 The Stock Option Problem -- 2 Stochastic Processes for Asset Price Modelling -- 3 An Initial Attempt at Pricing an Option -- 4 The Stochastic Differential Equation -- 5 Manipulating Stochastic Differential Equations and Stochastic Integrals -- 6 Ito's Lemma and Its Application -- 7 The Continuous Hedging Argument -- 8 Martingale Interpretation of No-Riskless Arbitrage -- 9 The Partial Differential Equation Approach Under Geometric Brownian Motion -- 10 Pricing Derivative Securities - A General Approach -- 11 Applying the General Pricing Framework -- 12 Jump-Diffusion Processes -- Option Pricing under Jump-Diffusion Processes -- 14 Partial Differential Equation Approach under Geometric Jump-Diffusion Process -- 15 Stochastic Volatility -- 16 Pricing the American Feature -- 17 Pricing Options Using Binominal Trees -- 18 Volatility Smiles -- Part II Interest Rate Modelling -- 19 Allowing for Stochastic Interest Rates in the B-S Model -- 20 Change of Numeraire -- 21 The Paradigm Interest Rate Option Problem -- 22 Modelling Interest Rate Dynamics -- 23 Interest Rate Derivatives - One Factor Spot Rate Models -- 24 Interest Rate Derivatives - Multi-Factor Models -- 25 The Heath-Jarrow-Morton Framework -- 26 The LIBOR Market Model.                   .