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Contribution Details

Type Master's Thesis
Scope Discipline-based scholarship
Title The Term Structure of Risk Aversion in Foreign Exchange Markets - An Analysis of Foreign Exchange Option Data over Varying Time Horizons
Organization Unit
  • Reto Willi
  • Thorsten Hens
  • Alexandra Janssen
  • English
Institution University of Zurich
Faculty Faculty of Business, Economics and Informatics
Number of Pages 37
Date July 2018
Zusammenfassung Problem Option markets allow us to learn about the market-implied preferences or expectations for different states of the world. Using these option data as a basis we can calculate the so-called state prices, which indicate how much agents value consumption in a specific future state of the world. Because options are available for several time horizons, it is possible to analyse these state prices over various maturities. Subsequently, we can calculate the investors' risk aversion from these option-implied state prices. Risk aversion is the behaviour of agents when exposed to uncertainty. Such an investor prefers a more predictable but possibly lower expected payoff over a more risky payoff. In many leading asset pricing models, it is assumed that agents' risk aversion is constant across various time horizons. Agents are supposed to trade off fixed payoffs and risky lotteries in the same way no matter whether the potential risk arises very close in the future or at a point in time in the more distant future. This prediction about agent's behaviour over different time horizons can be tested using option data. Furthermore, by studying option data at various fixed maturities we can show agents preferences towards risk at different time horizons. Method The thesis at hand analyses foreign exchange option data over different time horizons. First, we examine implied volatilities and the implied risk-neutral probability distributions. In particular, we interpolate the implied volatilities over various strike prices from a sound set of the most liquid currency pairs according to the method of Malz (1997). Moreover, from those implied volatilities we calculate the risk-neutral state prices to estimate risk-neutral forecast densities. Simultaneously, we create subjective belief distributions according to historical time series of foreign exchange rates. Finally, we compare the distributions to elicit the risk aversion of agents across different time horizons according to the method of Jackwerth (2000). Results Having analysed foreign exchange option data over different time horizons the thesis at hand found evidence that risk aversion varies across maturities. While many leading asset pricing models assume a constant risk aversion across time horizons this paper shows evidence for varying risk aversion in the foreign exchange market. In general, the risk aversion function of longer maturities behaves smoother across returns than for shorter horizons. In other words, the risk aversion calculated from shorter option contracts is more volatile than for longer maturities. Furthermore, for negative returns risk aversion is higher for shorter investment horizons than for longer ones. Although this paper could shed further light into the term structure of risk aversion in foreign exchange markets some questions remain unanswered. Additional research is needed to clearly illustrate why risk aversion in FX markets are not symmetrical across returns as expected. Moreover, the absence of a difference between direct and indirect quotation of exchange rates suggests taking results with caution. More research is clearly needed to bring further evidence to solve this puzzle.
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