Question

Assume that you use Purchasing Power Parity (PPP) to forecast exchange rates. Suppose you expect that inflation in the UK the next year will be 1.0%, and inflation in the US will be 5.0%. Assume that you are considering the purchase of five one-year British pound call options from PHLX with a strike price of $1.265/£. The premium is $0.014 per £. The spot rate of the pound is $1.25/£ and the one-year forward rate is $1.26/£ today.

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

2. Graph the call option cash flow schedule at maturity. Mark option’s strike price and break-even point.

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

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

Answer 1

a]

Expected spot exchange rate (in $/£) = current spot rate (in $/£) * (1 + US inflation) / (1 + UK inflation)

Expected spot exchange rate = 1.26 * (1 + 5%) / (1 + 1%) = $1.31/£

b]

The call option will have a profit if the spot price at maturity is more than $1.265/£.

Option Payoff = spot price at maturity - strike price - premium

If the spot price at maturity is less than or equal to $1.265/£, the loss equals the premium paid on the call option

The option cash flow at maturity is below :

c]

If the pound appreciates to expected future spot rate of $1.31/£, expected profit per call option = $0.031

expected profit on 5 call options = $0.031 * 5 = $0.155

d]

If the pound appreciates to forward rate of $1.26/£, expected loss per call option = $0.014

expected loss on 5 call options = $0.014 * 5 = $0.07