Risk Neutral Measure

Risk Neutral Measure is an important concept in the context of mathematical finance. It is regarded as a probability measure. Risk-neutral measure is normally employed in order to determine the worth of derivatives.
When it is presupposed that in the future the expected value of every financial asset would be the same as the final payments of the assets that have been discounted at a rate that is risk free, the concept of risk-neutral measure comes to the fore.

If the prices of assets are calculated taking into consideration the fact that there is no risk involved with them the resulting probability is known as risk-neutral measure.

Proposition of Risk-Neutral Measure
As per the risk-neutral measure it is taken for granted that all the assets would produce returns at an equal rate. It is assumed that their prices would not vary, which means the element of risk is absent. The risk-neutral measure is different from that of the Physical Measure.
As per the physical measure, the assets that have high levels of volatility of price, which means that they are more risky, can be expected to provide high levels of return. Their level of return is invariably higher than those assets that have lesser amounts of risk associated with them.
Uses of Risk-Neutral Measure
The worth of a derivative can be very conveniently conveyed in a formula by using risk-neutral measures.
Equivalent Martingale Measure
The risk-neutral measure is also known as the equivalent martingale measure. If in a specific financial market there are more than a single risk-neutral measure the use of the term equivalent martingale measure is considered to be more appropriate.

In case of equivalent martingale measure there is a price interval. In this interval there are no possibilities of any arbitrage.

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Last Updated on : 1st July 2013

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