FX Interest-Rate Differentials: Risk-Neutral and Real-World Drift
Summary
The document asks whether the difference between domestic and foreign risk-free rates determines an exchange rate’s drift only under risk-neutral pricing, or also describes real-world behavior. The question connects this distinction to two uses of simulation: valuing an FX option and estimating the real-world risk of an FX derivatives portfolio. It also asks whether persistent rate differences should correspond to sustained exchange-rate movements or eventual interest-rate convergence.
The response says that large differences in inflation and interest rates may accompany long-run currency depreciation in the real world, while presenting uncovered interest parity as a broader, contested hypothesis rather than a reliably established empirical rule. It notes that many forces move exchange rates, making the effect of rate differences hard to isolate. The Fisher effect and long-run purchasing power parity are also cited as relevant ideas. The discussion is qualitative and does not provide a drift estimator, empirical results, or a specific VaR modeling prescription.
Key ideas
- Risk-neutral FX drift for pricing and real-world FX drift for risk estimation are distinct modeling questions.
- Uncovered interest parity links interest-rate differences to expected exchange-rate changes but has contested empirical support.
- Many influences on exchange rates make the isolated effect of rate differentials difficult to measure.
- Inflation expectations and long-run purchasing power parity may contribute to long-term currency movements.
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Full text
# Is the differential between risk free rates the drift of an exchange rate only in the risk neutral world? # Is the differential between risk free rates the drift of an exchange rate only in the risk neutral world? Take for example this passage from "Monte Carlo Methods in Financial Engineering". Is this a result of the risk neutral world or is this the real world drift as well? I've never seen the explicit distinction made and I don't see anything in the argument that would imply it only to hold for the risk neutral world. Is this something that can actually be observed in the real world? If it were wouldn't we be seeing consistently rising (falling) FX rates between for example the USD and EUR (do we?) and if so wouldn't we expect the interest rates to start converging to each other as a result (do we?)? Put in another way, if we were to do a Monte Carlo value at risk simulation of the FX rate to capture the risk of FX derivatives, would we use this drift $\mu = r-r_f$? Or would we only use this drift if simulating the FX rate to, say, value a call option on the FX rate and use zero drift in the Value at Risk simulation (similar as to how we use r as the drift in equity option valuation and zero drift when performing a monte carlo value at risk simulation)? ## Answer by nbbo2 (score 2, accepted) https://quant.stackexchange.com/a/54675 Yes, clearly when 2 countries have widely different inflation rates and interest rates we do observe a deterioration of the exchange rate between them over the long term (in the real world, not risk neutral world). For ex. CHF vs USD for last 50 years. In Economics there is a hypothesis called the Uncovered Interest Parity which claims this is generally true for any country, this is more controversial and perhaps not always supported empirically. I am not familiar with the latest empirical studies. Exchange rates change all the time for 1000 reasons so it is sometimes difficult to pin down the role of just one factor like i.r. differences in an empirical study. But the tendency is there, I personally believe. The Fisher Effect (that the expected local inflation rate is incorporated into local interest rates) and long term PPP (Purchasing Power Parity) also play a role in this phenomenon and may be what drives it.
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