Question

A trader in New Zealand has purchased a European USD/NZD put to sell 1 million USD for 1.4 million NZD after 6 months. The US risk-free rate is 0.9%, compounded continuously, and the NZD risk free rate is 1.9%. The put premiun is NZD 0.041 million. If the current exchange rate is 1.37 NZD per US dollar, calculate the premium in NZD for a 6-month European call on 1 million USD, with strike at 1.4 million NZD.

Answer 1

To calculate the premium in NZD for a 6-month European call on 1 million USD with a strike at 1.4 million NZD, follow these steps: calculate risk-neutral probabilities, calculate the forward exchange rate, calculate the payoff of the call option, and calculate the premium in NZD.

Step-by-step explanation:

To calculate the premium in NZD for a 6-month European call on 1 million USD with a strike at 1.4 million NZD, we need to consider the interest rates and current exchange rate.

Here are the steps to calculate the premium:

1. Calculate the risk-neutral probabilities for the exchange rate using the interest rates:

• US risk-free rate: 0.9%, compounded continuously
• NZD risk-free rate: 1.9%

Calculate the forward exchange rate after 6 months:

• Forward rate = Current exchange rate * (1 + NZD risk-free rate) / (1 + US risk-free rate)
• Forward rate = 1.37 * (1 + 0.019) / (1 + 0.009)
• Forward rate = 1.3742

Calculate the payoff of the call option:

• If the exchange rate after 6 months is above the strike price, the payoff is (Exchange rate - Strike price) * Amount
• Payoff = (1.3742 - 1.4) * 1 million = -0.0262 million

Calculate the premium in NZD:

• Premium = Payoff - Put premium
• Premium = -0.0262 - 0.041
• Premium = -0.0672 million NZD