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School of Business  Department of Economics  Economics  2012
Thesis number: 13103
Implied crash risk in foreign exchange options  Analysis of EURUSD volatility curves
Author:  Karhapää, Henna 
Title:  Implied crash risk in foreign exchange options  Analysis of EURUSD volatility curves 
Year:  2012 Language: eng 
Department:  Department of Economics 
Academic subject:  Economics 
Index terms:  kansantaloustiede; economics; osakemarkkinat; stock markets; optiot; option; hinnoittelu; pricing; mallit; models 
Pages:  106 
Key terms:  foreign exchange options; implied volatility curve; currency crash; option pricing models; jumpdiffusion model 
Abstract: 
AALTO UNIVERSITY SCHOOL OF ECONOMICS ABSTRACT
Department of Economics December 2012
Henna Karhapää
IMPLIED CRASH RISK IN FOREIGN EXCHANGE OPTIONS  ANALYSIS OF EURUSD
VOLATILITY CURVES
Objective of the study
Objective of the study is to examine foreign exchange options and market expectations embedded in
option prices about the possibility of currency crashes. The thesis describes a procedure for
estimating the market assessment of currency crash risk from option implied volatility curves with
jumpdiffusion option pricing model for exchange rates. This method is used to construct time
series of optionimplied crash risk measures. Additionally, the study examines economic
determinants of implied crash risk over the period from January 5, 2006 to December 30, 2011.
Data
Data set consists of dollareuro foreign exchange option daily quotes of 1 month, 3 month, 6 month
and 1 year atthemoney volatilities, 25delta and 10delta risk reversals and 25delta and 10delta
butterfly spreads from January 5, 2006 to December 30, 2011. Each series contain 1562
observations for a total of 31 240 observations.
Results
Results show that shorter maturity options are pricing in higher frequency of jumps but lower
magnitude jumps, and the longer maturity options are pricing less frequent, higher magnitude
jumps. Jump volatility is increasing with maturity and jumps are found to contribute the most to the
prices of the longer options. The implied parameters are used to construct timeseries of three crash
risk measures: expected jumps per year, riskneutral skewness and crash probability. Expected
jumps per year, that indicates the frequency and the magnitude of jumps, is highest for the shortest
options and decreases as the time to maturity increases. During the sample period this crash risk
measure ranges from 9 percent to 27 percent. The riskneutral skewness measure indicates
asymmetry of the left and right tails of the riskneutral distribution. The yearly skewness
estimations range from 0,14 to 1,0. Crash probability indicates the optionimplied probability that
the exchange rate would depreciate more than a certain level during a time interval. Probability
estimates are calculated for three crash levels: 15 %, 20% and 25%.
The empirical section of this thesis shows that sovereign longterm bond yield, stock market and the
spot exchange rate are the best performing determinants of option implied crash risk. Crash risk
increases when the spread between US sovereign bond yields and euro area sovereign bond yields
increases. Higher crash risk is associated with relative underperformance of European stock market
compared to the US stock market. Weekly changes of the spot exchange rate are the best variable
explaining weekly changes of crash risk.
Keywords
Foreign exchange options, implied volatility curve, currency crash, option pricing models, jumpdiffusion
model

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