Background reading for modern asset pricing theory

Pricing models for financial derivatives require, by their very nature, utilization of continous-time stochastic processes. Three major steps in the theoretical revolution led to the use of advanced mathematical methods:

1. The arbitrage theorem gives the formal conditions under which "arbitrage profits" can or cannot exist. It is known that if asset prices satisfy a simple condition, then arbitrage cannot exit. This was a major development that eventually permitted the calculation of the arbitrage-free price of any "new" derivative product.

Black Scholes model: used the method of arbitrage free pricing. But the paper was also infleuntial because of the technical steps introduced in obtaining a closed form formula of option prices.

Using equivalent martingale measures was developed later. This method dramatically simplified and generalized the original approach of Black and Scholes. With these tools, a general method could be used to price any derivative product.

The value of derivatives often depends only on the value of the underlying asset, some interest rates, and a few parameters to be calculated. It is significantly easier to model such an instrument mathematically than, say, to model stocks. Some other books:

• Hull 93
• Jarrow and Turnbull (96)
• Ingersoll and Duffie (87 and 96)

Derivative securities are financial contracts that "derive" their value from the cash market instruments such as stocks, bonds, currencies and commodities. A financial contract is a derivative security, or a contingent claim if its value at expiration date T is determined exactly by the market price of the underlying cash instrument at time T.