Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It only takes a minute to sign up.
Sign up to join this community
We always regard precious metal as a FX rate e.g XAU/USD.
Is there any concept of spot rate for precious metal? If yes, then we know the dynamic of FX spot rate under risk neutral measure can be written as: $$\dfrac{dS}{S} = (r^d-r^f)dt + \sigma dW.$$ Here $r^d/r^f$ is domestic/foreign risk free interest rate. But for the precious metal e.g. XAU/USD, $r^d$ can be risk free interest rate of USD, what's $r^f$ here? Can anyone tell me the meaning in real market?
There is no interest rate associated with spot PMs. The reason why FX is evaluated in this way is because you can invest in short-term sovereigns (risk free rate) and get cash flow. So the FX rates are partially determined by the differentials between rates. PMs are quite different. If anything spot PMs are a negative yielding asset because of storage costs. There is a yield associated with the futures due to convenience yield / time value / demand for different tenors. It might be more useful from a valuation context to view gold as a commodity, not a currency.
