Question

Assume that you use Purchasing Power Parity (PPP) to forecast exchange rates. You expect that inflation in France the next year will be -1.0%, and inflation in the US will be +2%. Assume that you are considering the purchase of five one-year euro call options from PHLX with a strike price of $1.08/€. The premium is 0.5 cents per €. Today the spot rate of the euro is $1.06/€. The one-year forward rate is $1.07/€.

Based on your PPP analysis, what will be your expected spot exchange of $/€ in one year?

Graph the call option cash flow schedule at maturity. Mark clearly where will be option’s break-even point.

Determine your expected profit (or loss) if the euro appreciates to your expected future spot rate.

Determine your expected profit (or loss) if the euro appreciates to the forward rate.

(Note: One PHLX euro option contract covers €10,000. For simplicity, ignore the time value of money)

Answer 1

Solution:-

Step 1: Expected Spot Exchange based on PPP Analysis

Given:

Spot Rate is €1 = $1.06

Inflation in France is -1% and in US, it is +2%

Hence, according to PPP,

€1 * (1-0.01) = $1.06 * (1+0.02)

€0.99 = $1.0812

€1 = $1.0812/0.99

€1 = $1.0921

Hence, the expected spot exchange of $/€ in one year as per PPP Analysis is €1 = $1.0921

Step 2: Expected profit (or loss) if the euro appreciates to expected future spot rate

Given:

Strike price is $1.08/€

Premium is 0.5 cents per €

One PHLX euro option contract covers €10,000

Total Premium (payable today) = 0.5 cents * € 10,000 * 5 options = 25,000 cents = $250

Future Value of Premium = $250 * (1+0.02) = $255

Expected future spot rate is €1 = $1.0921

Expected profit on sale of € shall be

= (Expected future spot rate - Strike rate) * no. of euro per contract * no. of contracts

= ($1.0921 - $1.08) * 10,000 * 5

= $0.0121 * 50,000

= $605

Expected Net Profit = $605 - $255 = $350

Step 3: Expected profit (or loss) if the euro appreciates to forward rate

Given:

Strike price is $1.08/€

Premium is 0.5 cents per €

One PHLX euro option contract covers €10,000

Total Premium (payable today) = 0.5 cents * € 10,000 * 5 options = 25,000 cents = $250

Future Value of Premium = $250 * (1+0.02) = $255

Forward rate is €1 = $1.07

Expected profit (loss) on sale of € shall be

= (Forward rate - Strike rate) * no. of euro per contract * no. of contracts

= ($1.07 - $1.08) * 10,000 * 5

= - $0.01 * 50,000

= - $500

Net Profit = - $500 - $255 = - $755

Hence, Expected Net Loss = $755