eThesis - School of Business electronic theses

AALTO UNIVERSITY SCHOOL OF ECONOMICS ABSTRACT Department of Economics December 2012 Henna Karhapää IMPLIED CRASH RISK IN FOREIGN EXCHANGE OPTIONS - ANALYSIS OF EUR-USD 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 jump-diffusion option pricing model for exchange rates. This method is used to construct time series of option-implied 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 dollar-euro foreign exchange option daily quotes of 1 month, 3 month, 6 month and 1 year at-the-money volatilities, 25-delta and 10-delta risk reversals and 25-delta and 10-delta 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 time-series of three crash risk measures: expected jumps per year, risk-neutral 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 risk-neutral skewness measure indicates asymmetry of the left and right tails of the risk-neutral distribution. The yearly skewness estimations range from 0,14 to -1,0. Crash probability indicates the option-implied 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 long-term 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