2. Consider this reading carefully and then answer the questions that follow. A bank suggested risk reversals to investors that want to hedge their Danish krone assets, before Denmark’s Sept. 28 referendum on whether to join the Economic and Monetary Union. A currency options trader in New York said the strategy would protect customers against the Danish krone weakening should the Danes vote against joining the EMU. Danish public reports show that sentiment against joining the EMU has been picking up steam over the past few weeks, although the “Yes” vote is still slightly ahead. [He] noted that if the Danes vote for joining the EMU, the local currency would likely strengthen, but not significantly. Six- to 12-month risk reversals last Monday were 0.25%/0.45% in favor of euro calls. [He] said a risk-reversal strategy would be zero cost if a customer bought a euro call struck at DKK7.52 and sold a euro put at DKK7.44 last Monday when the Danish krone spot was at DKK7.45 to the euro. The options are European-style and the tenor is six months. Last Monday, six- and 12-month euro/Danish krone volatility was at 1.55%/ 1.95%, up from 0.6%/0.9% for the whole year until April 10, 2000, owing to growing bias among Danes against joining the EMU. On the week of April 10, volatility spiked as a couple of banks bought six-month and nine-month, at-the-money vol. (Based on Derivatives Week, April 24, 2000.)

(a) Plot the zero-cost risk reversal strategy on a diagram. Show the DKK7.44 and DKK7.52 put and call explicitly.

(b) Note that the spot rate is at DKK7.45. But, this is not the midpoint between the two strikes. How can this strategy have zero cost then?

(c) What would this last point suggest about the implied volatilities of the two options?

(d) What does the statement “Last Monday, six- and 12-month euro/Danish krone volatility was at 1.55%/1.95%,” mean?

(e) What does at-the-money vol mean? (See the last sentence.) Is there out-of-the-money vol, then?