
Risk-Neutral Measures
A risk neutral measure is a probability measure used in mathematical finance to aid in pricing derivatives and other financial assets. A risk-neutral measure for a market can be derived using assumptions held by the fundamental theorem of asset pricing, a framework in financial mathematics used to study real-world financial markets. Risk neutral measures give investors a mathematical interpretation of the overall market’s risk averseness to a particular asset, which must be taken into account in order to estimate the correct price for that asset. Because the assumption in the fundamental theorem of asset pricing distorts actual conditions in the market, it’s important not to rely too much on any one calculation in the pricing of assets in a financial portfolio. A risk neutral measure is a probability measure used in mathematical finance to aid in pricing derivatives and other financial assets.
What Are Risk-Neutral Measures?
A risk neutral measure is a probability measure used in mathematical finance to aid in pricing derivatives and other financial assets. Risk neutral measures give investors a mathematical interpretation of the overall market’s risk averseness to a particular asset, which must be taken into account in order to estimate the correct price for that asset.
A risk neutral measure is also known as an equilibrium measure or equivalent martingale measure.
Risk-Neutral Measures Explained
Risk neutral measures were developed by financial mathematicians in order to account for the problem of risk aversion in stock, bond, and derivatives markets. Modern financial theory says that the current value of an asset should be worth the present value of the expected future returns on that asset. This makes intuitive sense, but there is one problem with this formulation, and that is that investors are risk averse, or more afraid to lose money than they are eager to make it. This tendency often results in the price of an asset being somewhat below the expected future returns on this asset. As a result, investors and academics must adjust for this risk aversion; risk-neutral measures are an attempt at this.
Risk Neutral Measures and the Fundamental Theorem of Asset Pricing
A risk-neutral measure for a market can be derived using assumptions held by the fundamental theorem of asset pricing, a framework in financial mathematics used to study real-world financial markets.
In the fundamental theorem of asset pricing, it is assumed that there are never opportunities for arbitrage, or an investment that continuously and reliably makes money with no upfront cost to the investor. Experience says this is a pretty good assumption for a model of actual financial markets, though there surely have been exceptions in the history of markets. The fundamental theorem of asset pricing also assumes that markets are complete, meaning that markets are frictionless and that all actors have perfect information about what they are buying and selling. Finally, it assumes that a price can be derived for every asset. These assumptions are much less justified when thinking about real-world markets, but it is necessary to simplify the world when constructing a model of it.
Only if these assumptions are met can a single risk-neutral measure be calculated. Because the assumption in the fundamental theorem of asset pricing distorts actual conditions in the market, it’s important not to rely too much on any one calculation in the pricing of assets in a financial portfolio.
Related terms:
Arbitrage
Arbitrage is the simultaneous purchase and sale of the same asset in different markets in order to profit from a difference in its price. read more
Black-Scholes Model
The Black-Scholes model is a mathematical equation used for pricing options contracts and other derivatives, using time and other variables. read more
Capital Asset Pricing Model (CAPM)
The Capital Asset Pricing Model is a model that describes the relationship between risk and expected return. read more
Frictionless Market
A frictionless market is a theoretical trading environment where all costs and restraints associated with transactions are non-existent. read more
Heath-Jarrow-Morton Model (HJM)
A Heath-Jarrow-Morton (HJM) Model is used to model forward interest rates that are then used to find the theoretical value of interest-rate-sensitive securities. read more
Modern Portfolio Theory (MPT)
The modern portfolio theory (MPT) looks at how risk-averse investors can build portfolios to maximize expected return based on a given level of risk. read more
Risk-Neutral Probabilities
Risk-neutral probabilities are the odds of future outcomes adjusted for risk, which are then used to compute expected asset values. read more
Risk Averse
The term risk-averse describes the investor who prioritizes the preservation of capital over the potential for a high return. read more
Risk Neutral
Risk neutral is a mindset where an investor is indifferent to risk when making an investment decision. read more