Principles of Financial Engineering, 2nd Edition

CHAPTER 12

Some Applications of the Fundamental Theorem

1 Introduction

The theorem discussed in the previous chapter establishes important no-arbitrage conditions that permit pricing and risk management using Martingale methods. According to these conditions, given unique arbitrage-free state prices, we can obtain a synthetic probability measure, , under which all asset prices normalized by a particular Z_t become Martingales. Letting C(S_t, t) represent a security whose price depends on an underlying risk S_t, we can write,

(1)

As long as positive ...