Risk Neutral Pricing
Overview
Risk neutral pricing is one of the primary pricing frameworks for derivative pricing. It can be used
within the context of both discrete or continuous time models.
Intuition
The name risk neutrality is a reference to
utility based choice theory
in micro-economics. A risk neutral world is one in which all the participants have zero
risk aversion.
That is, the prices of assets do not reflect the riskiness of the asset in any sense. In such a world,
agents are indifferent between two assets with the same expected pay-offs, regardless of risk.
The arbitrage arguments used to price derivatives do not make any reference to the expected returns of
any of the assets involved. That is, when constructing the replicating portfolio, the trader
does not need to know the expected returns of the assets involved, only the risks.
That means that derivatives have the same price in the risk neutral world as the real world.
Frameworks
Examples
