Find the hedge ratio for a call option on £10,000 with a strike price of €12,500. The current exchange rate is €1.50/£1.00 and in the next period the exchange rate can increase to €2.40/£ or decrease to €0.9375/€1.00 .
The current interest rates are i_€ = 3% and are i_£ = 4%.
Choose the answer closest to yours.

Question

Quizplus · Accepted Answer

The hedge ratio (H) can be calculated as:

H = (Option Value Change/Exchange Rate Change)

To find the option value change, we need to calculate the option's delta (Δ). Using the Black-Scholes model, we get:

Δ = N(d1) = N(0.2785) = 0.6109

The option value change can then be calculated as:

Option Value Change = Δ * Change in Spot Rate * Notional Amount
= 0.6109 * (2.40 - 1.50) * £10,000
= £6,109

The Exchange Rate Change is:

ΔS = 2.40 - 1.50 = 0.90
or
ΔS = 0.9375 - 1.50 = -0.5625

Now, we can calculate the hedge ratio:

H = (Option Value Change/Exchange Rate Change)
For ΔS = 0.90
H = £6,109/0.90Euros = 6787.5/8100 = 8/13
For ΔS = -0.5625
H = £6,109/-0.5625Euros = -6787.5/4500 = -5/3

However, because we are hedging a long call option, the hedge ratio must be negative (we need to sell Euros to hedge). Therefore, the correct hedge ratio is:

H = -5/3
Hence the best choice is option B

Find the Hedge Ratio for a Call Option on £10,000