Risk reversals and strangles

A combination is an option portfolio containing both calls and puts. A spread is a
portfolio containing only calls or only puts. Most over-the-counter currency option
trading is in combinations. The most common in the interbank currency option
markets is the straddle, a combination of an at-the-money forward call and an atthe-
money forward put with the same maturity. Straddles are also quite common in
other over-the-counter option markets. Figure 1.24 illustrates the payoff at maturity
of a sterling–dollar straddle struck at USD1.60.
Also common in the interbank currency market are combinations of out-of-themoney
options, particularly the strangle and the risk reversal. These combinations
both consist of an out-of-the-money call and out-of-the-money put. The exercise
price of the call component is higher than the current forward exchange rate and the
exercise price of the put is lower.
In a strangle, the dealer sells or buys both out-of-the-money options from the
counterparty. Dealers usually quote strangle prices by stating the implied volatility
at which they buy or sell both options. For example, the dealer might quote his
selling price as 14.6 vols, meaning that he sells a 25-delta call and a 25-delta put at
an implied volatility of 14.6 vols each. If market participants were convinced that
exchange rates move as random walks, the out-of-the-money options would have the same implied volatility as at-the-money options and strangle spreads would be zero.
Strangles, then, indicate the degree of curvature of the volatility smile. Figure 1.25
illustrates the payoff at maturity of a 25-delta dollar–mark strangle.

In a risk reversal, the dealer exchanges one of the options for the other with the
counterparty. Because the put and the call are generally not of equal value, the
dealer pays or receives a premium for exchanging the options. This premium is
expressed as the difference between the implied volatilities of the put and the call.
The dealer quotes the implied volatility differential at which he is prepared to
exchange a 25-delta call for a 25-delta put. For example, if dollar–mark is strongly
expected to fall (dollar depreciation), an options dealer might quote dollar–mark risk
reversals as follows: ‘one-month 25-delta risk reversals are 0.8 at 1.2 mark calls
over’. This means he stands ready to pay a net premium of 0.8 vols to buy a 25-delta mark call and sell a 25-delta mark put against the dollar, and charges a net premium
of 1.2 vols to sell a 25-delta mark call and buy a 25-delta mark put. Figure 1.26
illustrates the payoff at maturity of a 25-delta dollar–mark risk reversal.

Risk reversals are commonly used to hedge foreign exchange exposures at low
cost. For example, a Japanese exporter might buy a dollar-bearish risk reversal
consisting of a long 25-delta dollar put against the yen and short 25-delta dollar call.
This would provide protection against a sharp depreciation of the dollar, and provide
a limited zone – that between the two exercise prices – within which the position
gains from a stronger dollar. However, losses can be incurred if the dollar strengthens
sharply.
On average during the 1990s, a market participant desiring to put on such a
position has paid the counterparty a net premium, typically amounting to a few
tenths of a vol. This might be due to the general tendency for the dollar to weaken
against the yen during the floating exchange rate period, or to the persistent US
trade deficit with Japan.