To analyze the future distribution of exchange rates, a model is needed. The most simple one is the so-called Garman-Kohlhagen model (a generalization of Black-Scholes for FX rates). It states that the random walk for the rate F satisfies
Getting Numbers for THE Swap.
As we have seen in A Short History of Floating Rates, historically the CHF rates were always lower (at least since the EUR exists) than the EUR rates, leading therefore to a negative drift rate (domestic minus foreign rate) and therefore to the expectation that the EUR will decrease compared to the CHF. (For the specialists in measure theory: in the risk neutral measure).
When we start a scenario generation at an FX rate of 1.65, we obtain with a volatility of 2% these possible outcomes after 10 years.
|Random paths as described above. 100 time steps of 0.1 years each|
Next week: Distirbution properties for the Garman Kohlhagen model