Question

Use the binomial option pricing model to find the value of 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 (i.e. u = 1.6 and d = 1/u = 0.625). The current interest rates are i_€ = 3% and are i_£ = 4%. Choose the answer closest to yours.

• €3,373

• €3,275

• €3,243

• €2,500

Answer 1

Binomial option pricing model is based on the concept of no arbitrage and used for pricing options. As per Binomial option pricing model, the assumption is

• There can be 2 possible values or prices for underlying asset i.e. price can either up or down
• Investors are risk neutral and the rate of interest remains fixed throughout the option lifecycle
• There are no taxes or transaction cost involved throughout the process

Given Strike Price = €12,500

Current exchange rate is €1.50/£1.00

Next period the exchange rate can increase to €2.40/£ or decrease to €0.9375/€1.00

Current interest rates are i_€ = 3% and are i_£ = 4%

Step - 1: Calculate the forward rate implied by the market condition.

Let’s assume F₁ (€/£) is the forward rate which is calculated as

= S₀ (€/£)*(1+ i_€) / (1+ i_£)

= 1.50 * (1+3%) / (1+4%)

= 1.4856 €/£

Step - 2: Calculate the € value of the £10,000 and the payoffs of the call options on £10,000 with a strike price of €12,500 in the two states, respectively.

In the up state: Value of £10,000

= S₀ (€/£)

= £10,000 * €2.40/£

= €24,000

The payoff of the call

= MAX [S₀ (€/£) – X, 0] where X is strike price

= MAX [€24,000 - €12,500, 0] = €11,500 (in-the-money)

In the down state: Value of £10,000

= S₀ (€/£)

= £10,000 * €0. 9375/£

= €9,375

The payoff of the call

= MAX [S₀ (€/£) – X, 0] where X is strike price

= MAX [9,375 – 12,500, 0]

= 0 (out-of-money)

Step - 3: Calculate the risk-neutral probability in the up state (set to q).

£10,000 * €1.4856/£ = q * 24,000 + (1-q) * 9,375€

q = (14,856.00-9,375) / (24,000-9,375) = 0.3748.

Step – 4: Calculate the value of the call option on £10,000

C₀ = € 0.3748 * 11,500 / (1+3%) = €4184.317

Hence the correct answer is €3,373