This tutorial will take you step by step through computing both the implied volatilities and hedge parameters for currency options. You can complete the tutorial online by using our currency option calculator. You should first recreate the numbers in this tutorial and then apply the same steps to the currency option markets of your choice.

The Wall Street Journal provides information regarding USD LIBOR. We will use this information with currency forward prices to get an estimate for the foreign offering rate as illustrated in the previous Tutor break.

Aside: In the following examples the closest LIBOR rate is applied for example purposes only. No interpolation method is used.

Problem: What is the implied volatility and the Greeks for a Deutschmark currency option trading on the Philadelphia exchange?

Data: Close of trading October 30, 1996

Reported USD LIBOR rates in the WSJ: 1-month 5 3/8%, 3-months 5 ½%

Step 1: Select the subject Option Calculator in Option Tutor. From the menu item Options select the sub-menu item calculator. Click on LIBOR and enter the following LIBOR rate information:

That is, the continuously compounded equivalent rate for the US is 0.05437. Click on Transfer to transfer this rate to both the option calculator and the futures calculator.

Step 2: For the close of trading October 30, the 30-day forward price = 0.6628, and the spot exchange rate = 0.6616. Select Options from the menu item in Option Calculator and then select the sub menu item Futures Calculator. In the regular calculator enter the 30-day life in the Convert Dates into Maturity and transmit to the future's calculator by clicking on the button Convert and then Transmit:

Step 3: The futures calculator now has the time to maturity and the US interest rate. Select Currencies in the Future's calculator and enter the spot exchange rate (0.6616) and forward exchange rate (0.6628) as displayed below. Finally, for this step select Implied Foreign Int. Rate and then click on Calculate. Your futures calculator is as follows:

The implied rate for Germany is 0.033 from 30-day forwards on October 30, 1996.

Step 4: The goal of this next step is to enter this data into Option Tutor's Option Calculator to solve for implied volatility and the Greeks from the option price.

Data: Trading terminates 2^nd Friday before 3^rd Wednesday of the month. That is, they are exercised at the prices realized on this day. This day is November 15, 1996 which when expressed as proportion of a year equals 0.043836.

66 Nov Put 0.22, Strike price = $0.66 USD for DEM 1, premium 22 units = $6.25 * 22 = $137.50

Underlying = 62,500*0.6616 = 41,350, Strike = 62,500*0.66 = 41,250

European style options

The implied volatility and Greeks are as displayed below:

Step 5: Consider the same problem as above but this time for an American, December maturity option.

Data: 66 Dec Put 0.57, Strike price = $0.66 USD for DEM 1, premium 57 units = $6.25 * 57 = $356.25

Expiration is 3^rd Wednesday of December, (December 18, 1996 = 0.13427)

American style

Assume that the same interest rates apply to this problem i.e., flat from end of November to middle December. This is a reasonable simplifying assumption if you contrast the 1-month and 3-month LIBOR rates at this time (5 3/8 for 3-months vrs 5 ½ for 3-months)

The trinomial tree numerical procedure is used first for 100, and then 1000 steps (time partitions). For 100 steps these estimates are:

and for 1000 steps these estimates are:

You can check that this method is very accurate even with as few as 100 partitions.