<div class="post">

	<p>Background reading for modern asset pricing theory</p>

	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:


	<li>
	<ul>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.</ul>

	<ul>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.</ul>

	<ul>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.</ul>

	</li>

	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:
	<ul>
	<li>Hull 93</li>
	<li>Jarrow and Turnbull (96)</li>
	<li>Ingersoll and Duffie (87 and 96)</li>
	</ul>

	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.

</div>