Съдържание:
  • Financial derivatives : a brief introduction
  • A primer on the arbitrage theorem
  • Calculus in deterministic and stochastic environments
  • Pricing derivatives : models and notation
  • Tools in probability theory
  • Martingales and martingale representations
  • Differentiation in stochastic environments
  • The Wiener process and rare events in financial markets
  • Integration in stochastic environments : the Ito integral
  • Ito's lemma
  • The dynamics of derivative prices : stochastic differential equations
  • Pricing derivative products : partial differential equations
  • The Black-Scholes PDE : an application
  • Pricing derivative products : equivalent martingale measures
  • Equivalent martingale measures : applications
  • New results and tools for interest-sensitive securities
  • Arbitrage theorem in a new setting : normalization and random interest rates
  • Modeling term structure and related concepts
  • Classical and HJM approaches to fixed income
  • Classical PDE analysis for interest rate derivatives
  • Relating conditional expectations to PDEs
  • Stopping times and American-type securities.