# Rational Pricing

Rational pricing is an assumption that states that the asset pricing models will show the arbitrage free pricing of assets because any deflection from the asset price would be “arbitraged away”. The rational pricing assumption is used while pricing for the fixed income securities such as bonds is done.
The theory is also fundamental to pricing the derivative instruments. Rational pricing approach is highly used in pricing the fixed rate bonds. With the given fact that the cash flows may be replicated, the bond price must be equal to the additions of all the cash flows that are discounted at the rate at which the corresponding government securities are discounted.

The discounted rate here is also known as the corresponding risk free rate. If this were not the case, arbitrage would pull the price again to the line where the pricing is based on securities issued by the governments.

The rational pricing can be explained mathematically by the following formula:

P0 = Σ(Ct/(1+rt)t), where the summation takes the value of t varying from 1 to T.

Here,

Ct stands as the cash flow

Ct is discounted at the rate of rt
The above mathematical formula is also often expressed as:

P0 = Σ C(t) � P(t), where the summation takes the value of t varying from 1 to T.

In the second formula, instead of rate, prices are used, as the prices are more easily available.

The derivatives are financial instruments that allow for the selling and buying of the same assets on the two markets – the derivatives market and the spot market. According to the principle of rational pricing, any imbalance between the prices in two markets would be arbitraged away. Hence, for a derivative contract that is correctly priced, the strike price or the reference rate, the price of derivative and the spot price are related in such ways that arbitrage is not possible. The basic concept of the theory is to gain the arbitrage free pricing of derivatives. 