Derivative Security Pricing

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.