Saturday, August 27, 2005

Dynamical hedging and Black-Scholes

Derman and Taleb claim that you can derive Black-Scholes without assuming instantaneous replication of the option using cash and stock. (This assumption has some practical limitations in the real world.) I always thought the replication insight very important for justifying the use of the riskless rate to discount cash flows. As the authors note, formulae equivalent to B-S were derived by others such as Samuelson, but leaving the discount rate as an unknown parameter. Once you know the option can be perfectly hedged, it becomes straightforward to price it given any model in which you can compute the expected return.

For elementary discussion, see here.

No comments:

Blog Archive