The economic-political instability of a country, which is tied to its credit risk, often leads to sharp depreciation and heightened volatility in its currency. This paper shows that not only the creditworthiness of the euro-area countries with weaker fiscal positions but also that of the member countries with more sound fiscal positions are important determinants of the deep out-of-the-money euro put option prices, which embedded information on the euro crash risk during the sovereign debt crisis of 2009–2010. Using information on the option prices under the stochastic-volatility jump-diffusion model, the euro’s crash probability of 11% in a year with crash size of 14% is estimated at the end of April 2010. However, during the period of the global financial crisis between the Lehman default and September 2009 before the debt crisis began, the estimated crash size reflects the potential sharp devaluation of the US dollar that might result from quantitative easing in the US.