Currency, Money Market Accounts, and Risk-Neutral Numeraires

Summary

The document raises a conceptual question about the choice of numéraire when defining a risk-neutral measure in currency markets. It challenges the statement that the money market account, rather than currency itself, is the relevant numéraire because holding currency can earn interest after it is invested in a money market account. The question compares this with a bond, which can also be exchanged for cash and invested.

The author asks how the description of currency as paying a dividend should be understood and whether converting a money market account into another currency changes the argument. No answer or derivation is included, so the document does not resolve how currency carry, domestic and foreign money market accounts, and tradable numeraires fit together. Its value is as a prompt to clarify numéraire conventions in foreign exchange pricing; readers need an external explanation to obtain the underlying measure-change framework.

Key ideas

• The document questions why currency is described as paying a dividend in numéraire discussions.
• It compares holding currency with holding a bond that can be converted to cash and invested.
• It asks how exchanging and reinvesting cash across currencies affects the choice of numéraire.
• No answer is provided, so the measure-change reasoning remains unresolved in the source.

Tags

# Why a currency is not considerend as a numéraire for a risk neutral measure


# Why a currency is not considerend as a numéraire for a risk neutral measure












We often say that "A risk neutral measure is associated with the money market account, not the currency. Currency pays a dividend because it can be invested in the money market."

How is a currency paying a dividend ? if like it is advocated, investing it in a money market makes it paying dividend, isn't it the same with the bond? We could exchange the bond for an amount of currency and invest it in money market so to generate a dividend, but we still use a bond as a numéraire and define a risk-neutral measure with it !!! or simply converting a money market account in a nother currency and then reinvest the cash in a money market account ? !! I'm missing something

thank you

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.