Principles of Financial Engineering, 3rd Edition

Chapter 13

Some Applications of the Fundamental Theorem

This chapter discusses three applications of the fundamental theorem and critically evaluates them in the light of real-life complications. First, we discuss Monte Carlo methods for option pricing including binary FX options. We show how path dependence can be incorporated into Monte Carlo simulations. Second, we explain how stochastic differential equations and tree models can be calibrated to market data using the fundamental theorem. We present the Black–Derman–Toy model and introduce caplets and caps before discussing how to price them. Third, we show how the fundamental theorem can be used for pricing quanto securities such as quanto forwards and options whose price depends on correlations ...