Modeling Derivatives in C++
Chapter One
Black-Scholes and Pricing Fundamentals
This chapter discusses the most important concepts in derivatives models, including
risk-neutral pricing and no-arbitrage pricing. We derive the renowned Black-
Scholes formula using these concepts. We also discuss fundamental formulas and
techniques used for pricing derivatives in general, as well as those needed for the remainder
of this book. In section 1.1, we discuss forward contracts, the most basic
and fundamental derivative contract. In section 1.2, we derive the Black-Scholes
partial differential equation (PDE). In section 1.3, we discuss the concept of riskneutral
pricing and derive Black-Scholes equations for European calls and puts using
risk-neutral pricing. In section 1.4, we provide a simple implementation for
pricing these European calls and puts. In section 1.5, we discuss the pricing of
American options. In section 1.6, we discuss fundamental pricing formulas for derivatives
in general. In section 1.7, we discuss the important change of numeraire
technique-useful for changing asset dynamics and changing drifts. In section 1.8,
Girsanov's theorem and the Radon-Nikodym derivative are discussed for changing
probability measures to equivalent martingale measu ... read full excerpt from Modeling Derivatives in C++ ebook
