The CHF/EUR exchange rate during the Swiss National Bank's minimum exchange rate policy: a latent likelihood approach

Abstract

Our model treating the rate bound in terms of a put option accurately predicts the CHF/EUR exchange rate following the removal of the lower bound of 1.20

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 See http://www.snb.ch/en/mmr/reference/pre_20110906/source/pre_20110906.en.pdf for the original SNB press release.

2 See ‘Why the Swiss unpegged the franc’, The Economist, January 18, 2015.

3 Note that a model where τ is exponentially distributed does not nest our model specification.

4 An even stronger result can be obtained if the interest rate is zero and the dividend yield is positive. In this case, an American put option should never be exercised early, making its price equal to that of a European put option. This is a lesser-known dual to Merton's old result about never exercising American call options before maturity when there are no dividends and the interest rate is positive. In obvious notation (and with i denoting the dividend yield, which corresponds to the foreign interest rate in our setting) the proof follows from put/call-parity: $P^A\left(t\right)\ge P^E\left(t\right)\ge P^E\left(t\right)-C^E\left(t\right)=K-\exp (-i\tau )V_t\ge K-V_t$, hence put options are always worth more alive than exercised under these assumptions.

5 Lera et al (2017) generalize our approach and show that (two-sided) target zones can be modeled as an infinite series of ‘mirrored’ American put- and call-options. While our choice of a geometric Brownian motion for the latent exchange rate in connection with a one-sided target zone allows for analytical tractability, they resort to numerical solution techniques, which allows them to relax both assumptions.

6 We can let $v_0$ be the last observation before the guarantee was enforced and thus – unlike Lando (2004) – avoid maximizing over it. Also, because μ does not enter the N-term, we can (and do) ‘profile it out’: $\mu =\ln \left(v_n/v_0\right)/(t_n-t_0)$.

7 Results are available upon request.

8 Robustness checks reveal that longer estimation windows of 4 and 6 months lead to qualitatively similar results, whereas shorter estimation windows make volatility estimates very noisy.

9 Note that at any given date after early December 2011 (= September 6, 2011 + 3 months), these estimates can be calculated using only information available up to that date.

10 The likelihood-nature of the estimation leads to a difference between full sample parameter estimates and simple averages of time-dependent estimates.

11 See for instance Commerzbank's market view ‘SNB damages own credibility’ on December 18, 2014, http://tradingview.today/forex/snb-damages-own-credibility