Some Applications of the Fundamental Theorem
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 Zt become Martingales. Letting C(St, t) represent a security whose price depends on an underlying risk St, we can write,
As long as positive ...