13.4 Applications:
Currency Options
13.4 Applications:
Currency Options
Three popular types of currency options are:
European options traded on the exchange rate (Philadelphia Stock
Exchange), American options traded on the exchange rate (Philadelphia Stock
Exchange), and American options traded on currency futures (Chicago Board
Options Exchange). For currency
options, the last trading day is the Friday before the third Wednesday of the
settlement month. For options on the futures, the last trading day is the second
Friday before the third Wednesday. Settlement
is on the Saturday.
Online, you can apply the Option Calculator to value some
currency option examples. We will
assume that the strike currency is the U.S.$ and the delivery currencies are
pounds, Deutschmarks, and the yen. For
the former two (pounds and Deutschmarks) option values have been driven by
speculation as to whether Europe's Exchange Rate Mechanism (ERM) (The ERM was
first formed on March 13, 1979 to manage target ranges for the exchange rates of
member countries.) will hold together or not.
For example, the British pound joined the ERM on October 8,
1990, but pulled out (along with the Italian lira) on September 16, 1992.
This precipitated a currency crisis in which the implied volatilities for
pounds and Deutschmarks rose from the 11%-12% range to over 20% by the end of
October. Implied volatilities then
fell back sharply during 1993. Pressure
again built up for a realignment of target ranges when the German Bundesbank
failed to deliver interest rate cuts on Thursday, July 29, 1993.
The foreign exchange market response was again hectic, leading to heavy
intervention by the European central banks to support ERM targets as required by
ERM regulations. Ultimately, the
mark/franc targets were adjusted to resolve this issue.
This was followed by implied volatilities settling down to just above
historic levels.
In this situation, the Black-Scholes assumption of constant
volatility was clearly violated. Furthermore,
it is unlikely that projected volatilities will remain constant as we move
across different option maturities because of potential currency crises.
To apply the model, we need to make an assumption about
volatilities. During the period we are examining, there was no currency crisis.
For the purposes of this exercise, we will use the historical level of
11% for the Deutschmark.
Assume the values in Table 13.11 as reported in The
Wall Street Journal on March 31, 1994
(closing prices for March 30, 1994, Philadelphia Exchange).
Using the information in Tables 13.11 and 13.12, combined with the LIBOR
information, let's calculate currency option values.
First, we'll provide some examples to step you through the
details.
Table 13.11
Currency Option Values
|
Country |
Strike |
Maturity |
Calls |
Puts |
|
|
Britain
European |
140 |
June |
|
0.59 |
|
|
31,250p |
147.5 |
April |
|
1.06 |
|
|
|
150 |
April |
0.40 |
|
|
|
American |
142.5 |
June |
|
0.83 |
|
|
|
145 |
May |
|
0.65 |
|
|
|
147.5 |
April |
|
0.98 |
|
|
|
147.5 |
May |
|
1.80 |
|
|
|
147.5 |
June |
2.45 |
|
|
|
|
150 |
April |
0.40 |
|
|
|
|
150 |
June |
1.50 |
|
|
|
|
152.5 |
April |
0.13 |
|
|
|
|
152.5 |
May |
0.40 |
|
|
|
|
155 |
June |
0.44 |
|
|
|
Germany |
59 |
April |
1.07 |
|
|
|
European |
59 |
April |
0.90 |
0.28 |
|
|
|
59 |
June |
|
0.94 |
|
|
American |
56 |
June |
|
0.18 |
|
|
|
57 |
June |
2.87 |
|
|
|
|
58 |
April |
|
0.08 |
|
|
|
58 |
June |
|
0.54 |
|
|
|
58.5 |
April |
|
0.17 |
|
|
|
58.5 |
May |
|
0.44 |
|
|
|
58.5 |
June |
|
0.76 |
|
|
|
59 |
April |
0.84 |
0.26 |
|
|
|
59 |
June |
|
0.94 |
|
|
|
59.5 |
April |
0.56 |
0.44 |
|
|
|
59.5 |
June |
1.05 |
1.13 |
|
|
|
60 |
April |
0.36 |
|
|
|
|
60 |
May |
|
1.18 |
|
|
|
60 |
June |
|
1.43 |
|
|
|
60.5 |
April |
0.19 |
|
|
|
|
60.5 |
May |
0.48 |
|
|
|
|
60.5 |
June |
0.66 |
|
|