In mathematical finance, a risk-neutral measure,is a probability measure that results when one assumes that the current value of all financial assets is equal to the expected value of the future payoff of the asset discounted at the risk-free rate. The concept is used in the pricing of derivatives.
It is important to note that clearly the probabilities over asset outcomes in the real world cannot be impacted; the constructed probabilities are counterfactual. They are only computed because the second way of pricing, called risk-neutral pricing, is often much simpler to calculate than the first.
The main benefit stems from the fact that once the risk-neutral probabilities are found, every asset can be priced by simply taking its expected payoff (i.e. calculating as if investors were risk neutral). If we used the real-world, physical probabilities, every security would require a different adjustment (as they differ in riskiness).
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
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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