# What is the intuition behind the equivalent martingale measure result?

"Suppose that f and g are the prices of traded securities dependent on a single source of uncertainty and define phi = f/g. The equivalent martingale measure shows that, when there are no arbitrage opportunities, phi is a martingale for some choice of the market price of risk. What is more, for a given numeraire security g, the same choice of the market price of risk makes a martingale for all securities f. This choice of the market price of risk is the volatility of g." (Hull pg 636)

I've seen the proof of this result in Hull, and it is clear mathematically. However, I am having trouble explaining the intuition behind EMM without resorting to the mathematical proof.

Say you needed to explain it non-technically to an investor. How would you describe the general concepts behind EMM, (such as the choice of the numeraire, market price of risk, volatility of g, forward risk neutrality) and intuitively why EMM makes sense?

• Sorry for asking but did you look for existing SE questions? There are suite a bunch dealing with this particular issue. If so, please state what is it exactly that bothers you. – Quantuple Oct 4 '16 at 20:43
• I suppose what I'm confused about is how to articulate why specifically EMM differs from Risk Neutral Valuation in general; when it is appropriate to use martingale pricing instead of risk neutral pricing; and why, intuitively, using the numeraire whose volatility = the market price of risk transforms f/g into a martingale. It's unclear to me how I would describe this last part in particular without having to show the mathematical proof eliminating the drift term (ie how to explain it non-technically) – beeba Oct 5 '16 at 14:01
• Risk neutral valuation = Maringale pricing. It precisely uses the concept of equivalent martingale measure (EMM), so I do not know what you mean exactly. – Quantuple Oct 5 '16 at 14:33