The City Swap Conclusions

For the last weeks, I have been quite actively writing on the city swap (see VaR and expected shortfall of the city swap and the posts quoted there). This post is about drawing my conclusions.

A Short History
The swap between the city and the bank was entered in 2007; the structured leg had a strong coupon dependence on the CHF/EUR exchange rate. With the CHF getting stronger and stronger (especially in 2011), the city refused to continue payments in Oct. 2011, claims and counterclaims were filed, and it is still open how the trial at the commercial court will end.

The Legal Dispute
The city argues that the bank should have known that the city had not been allowed to enter the swap. I am not an attorney and will not publish my personal opinion here.

The Mathematics of Valuation
I have shown in several posts on Garman-Kohlhagen that already the most simple model (Garman-Kohlhagen) is capable of delivering indicatively reasonable valuation (of course, depending heavily on the volatility) and to reveal the strong asymmetry in the payoff, meaning that the city can gain only a small portion but can have severe losses if markets are unfavorable (which is what happened since 2011).

Higher Sophistication Necessary?
Of course, one could use much more complicated models (local volatiliy or stochastic volatility for the FX process, randomness of interest rates). The valuation results will then differ quantitatively from the Garman Kohlhagen values, but in any case the main price driver will be the FX rate at the respective valuation date. Due to the extreme leverage of the termsheet, any pricing model will deliver magnificent losses at the current exchange rate of (more or less) 1.2 CHF per EUR.

Risk Analysis
From my point of view, a simple VaR based Risk analysis (again based on the Garman Kohlhagen model) could have pointed out that in 5 percent of the cases, losses in the order of 9 digit sums can and will occur. The counterclaim of the bank claims for more than 400 million EUR. You can buy 1000 decent 1000 square foot apartments in Linz for that price.

To Summarize
There is no need to have rocket science modelling for analysing the riskiness of the specific swap. When it was entered, the CHF was very cheap compared to the EUR, and volatilities were very low. The strengthening of the CHF and the increase in volatilities, both induced by the EUR crises, led to the negative explosion of the valuation results.