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...