Cross Economic Determinants of Implied Volatility Smile Dynamics: Three Major European Currency Options

• Published date: 01 November 2016
• Date: 01 November 2016
• DOI: http://doi.org/10.1111/eufm.12072

Cross Economic Determinants of

Implied Volatility Smile Dynamics:

Three Major European Currency

Options

Qian Han, Jufang Liang and Boqiang Wu

The Wang Yanan Institute for Studies in Economics (WISE), National Key Lab of Econometrics,

Xiamen University, Xiamen, China, P.R.

E-mails: hanqian@gmail.com; Jufangliang@stu.xmu.edu.cn; wuboqiang@gmail.com

Abstract

This paper examines the contemporaneous and lead–lag relationships between

economic variables and implied volatility smiles for three major European

currency options. We find that cross economic determinants are at least as

important as own economic variables in explaining the dynamics of implied

volatility smiles. Out-of-sample tests also suggest that cross economic variables

are important in predicting an economy’s currency option smile. These findings

suggest that the price impact from cross economic determinants may help fill the

gap between the theoretical and the practical implied volatility skews.

Keywords: implied volatility smile, economic determinants, currency options

JEL classification: G13

1. Introduction

The relationship between asset returns and the real economy has been widely studied for

different financial markets. Fama (1990) and Schwert (1990) find that real stock returns

contain rich information about future production growth rates. Estrella and Mishkin

The authors thank Robert I. Webb (the discussant) and other participants in the 3rd

International Conference on Deri vatives and Risk Management for thei r valuable

discussions and comments. We also thank the anonymous referee and the Editor for their

very constructive comments and suggestions. Han’s research is supported by the National

Science Foundation of China (project no. 71471153). Liang’s research is supported by

Overseas Visit Project of Xiamen University Graduate School. Part of his work was

completed during his visit to the University of North Carolina at Charlotte. All errors, if

any, are those of the authors.

European Financial Management, Vol. 22, No. 5, 2016, 817–852

doi: 10.1111/eufm.12072

© 2015 John Wiley & Sons, Ltd.

(1998) examine the out-of-sample performance of several financial variables, including

stock prices, in predicting US recessions. Stock and Watson (1999, 2003) show that

asset prices can be used to forecast inflation and output. Hong and Yogo (2012) argue that

open interest of commodity futures is more informative about future economic activity

than futures prices. Welch and Goyal (2008) and Rapach et al. (2013) investigate the out-

of-sample predictability of real economic variables on equity premium. Beber and

Brandt (2006) examine the effect of macroeconomic news announcements on the

moments of risk-neutral state price densities extracted from bond options markets.

Ludvigson and Ng (2009) find significant predictive power of real activity for bond risk

premia.

This paper studies the cross asset–economy relationship, i.e., how asset prices in one

country or region may be affected by or contain predictive information about economic

variables in another country or region.

1

Specifically, we examine the role of own, and in

particular cross, economic determinants on three major European currency option

implied–volatility–smile (IVS) dynamics. These options are over-the-counter (OTC)

options for euro (EUR), British pound (GBP) and Swiss franc (CHF), all quoted against

US dollars (USD). We address three questions. Which own and cross economic variables

are relevant to explain the contemporaneous dynamics of the three currency option IVS

dynamics? Are there any Granger causality relationships between each of these

economic variables and the currency option IVS dynamics? Are cross economic

variables important in the out-of-sample predictions of the currency option IVS

dynamics?

To answer these questions, we first use the option price quotes, i.e., at-the-money

(ATM) volatility, risk reversal (RR) and butterflyspread(Bfly), to capture the

shape of the IVS. The ATM corresponds to the level of the smile curve, RR describes

the asymmetry of the curve and Bfly proxies the curvature of the curve. We further

propose that RR measures net speculative demand (NSD) and Bfly is a measure

of the gross hedging pressure (GHP) of the corresponding currency. The

economic determinants we consider are largely taken from the literature and can

be divided into three groups: variables from the foreign exchange market, from the

stock market and from the bond market. We use ordinary least squares (OLS)

regressions to test the contemporaneous correlations between curve characteristics

and own or cross economic variables, and then apply a multivariate autoregres-

sive regression (VAR) analysis to examine their Granger-causality relationships.

Impulse response and variance decomposition analyses are conducted as robustness

checks.

We find that cross economic variables are at least as, sometimes more, important

determinants of currency IVS dynamics than their own economic variables.

Contemporaneously, historical volatilities of currencies are positively associated with

ATM volatilities of other currencies. A negative spot rate return in one currency market

is accompanied by an increase in the ATM volatilities of other currencies. The

1

The economic variables studied in this paper are not strictly real economic activity proxies.

Rather, they are variables from the financial markets. However, the literature of empirical

option pricing has termed them ‘economic determinants’to differentiate these determinants

from the underlying asset characteristics. We use this term to keep consistency with this line

of research.

© 2015 John Wiley & Sons, Ltd.

818 Qian Han, Jufang Liang and Boqiang Wu

Switzerland stock market characteristics are closely associated with the RR and Bfly for

the pound and euro. And default risk in the euro bond market seems highly associated

with the implied volatilities of the Swiss franc and the pound.

The importance of cross economic variables is also shown in the Granger-causality

tests. For example, the historic volatility of the stock index in the euro area has predictive

power for the butterfly spread of the pound. The pound spot return Granger-causes the

risk reversal of all three options. The risk reversals of the euro and pound both positively

Granger-cause the spot rate trends of the other two currencies. Default spread does not

play any role in the Granger causality tests for butterfly spread and risk reversal but is

very important for ATM volatility. The ATM volatilities of the Swiss franc and the euro

Granger-cause the default spreads for all three economies. Both the impulse response and

variance decomposition analyses confirm our findings. In particular, the variance

decomposition analysis, which explicitly quantifies the magnitudes of contributions to

the forecast error variance of the smile dynamics of both own and cross economic

variables, finds a more significant role played by cross economic variables. Because

previous studies claim that in-sample analyses may be unreliable due to over-fitting

concerns, we also conduct out-of-sample tests to examine the predictive power of cross

economic variables. The results suggest that cross economic variables are at least as

important in predicting an economy’s currency option smile dynamics out-of-sample as

its own economic variables.

Why is a country’s currency option IVS dynamics significantly determined by another

country’s economic variables? The unprecedented speed of economic and financial

globalisation over the past few decades seems to be a plausible reason. Economic

interaction among different countries and regions has soared, and financial markets

around the world have seen increased return correlations, volatility spillover and risk

contagion. Rizova (2010) shows that, in a two-country, Lucas-tree model with

information diffusion, returns in one country can predict returns in a trading partner

country. European economic integration is probably the most successful regional

integration so far in history and European Union countries trade heavily with each other

due to historical and geographical bonds among union members. Table 1 lists the top

trading partners for the three nations under consideration. For the UK, the European

Union dominates other countries and regions in both imports and exports, while

Switzerland is ranked 3rd in exports and 5th in imports. The EU and Switzerland are each

other’s major trading partners with over 50% (74%) of exports (imports) of Switzerland

going to (coming from) the EU. In theory, these close trade ties will facilitate information

diffusion across the three economies, leading to Granger-causal relationships between

their asset prices.

In addition, macroeconomists tend to agree that currency value is a good economic

indicator. If this is the case, then the progress of economic integration should strengthen

relationships between currency returns, consequently increasing the correlation between

currency option prices. In fact, as shown in Figure 1, the correlation between USD/EUR

and USD/CHF returns is as high as 72% (USD/EUR and USD/GBP is 65% while USD/

CHF and USD/GBP is 42%).

An alternative explanation is that, as pointed out in Rapach et al. (2013), information

diffuses from the market with the most investor attention to other markets. The three

currencies in this study are all among the most actively traded and most influential

currencies in the global foreign exchange market. Indeed, the euro is the major

alternative reserve currency after the US dollar, the Swiss franc is commonly perceived

© 2015 John Wiley & Sons, Ltd.

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