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 (delta) for a call option is given by the formula:

delta = N(d1)

where N() represents the cumulative standard normal distribution, and d1 is the standardised variable given by:

d1 = [ln(S/X) + (r + σ^2/2)t]/(σ√t)

where S is the spot exchange rate, X is the strike price, r is the domestic interest rate, σ is the volatility of the exchange rate, and t is the time to expiration of the option.

Using the given values, we have:

S = €1.50/£1.00 = 1.50

X = €12,500/1.50 = £8,333.33

r = 4%

σ = (2.40 - 0.9375)/2 = 0.75125

t = 1

Substituting into the formula, we get:

d1 = [ln(1.50/8,333.33) + (0.04 + 0.75125^2/2)]/(0.75125√1) = 0.4016

Using a standard normal distribution table, we find that N(d1) = 0.6557

Therefore, the hedge ratio is:

delta = N(d1) = 0.6557

rounded to the nearest whole number, this is 8/13, which is closest to answer choice B).

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