Question

On June 1, the 4-month interest rates in Switzerland and the United States were, respectively, 2% and 5% per annum with discrete compouding. The spot price of the Swiss franc was $0.8000/CHF. You took a short position of a CHF forward, CHF 100,000, delivery on October 1. One month later on July 1, three-month interest rates in Switzerland and the United States were, respectively, 2.5% and 4.5% per annum with discrete compouding. The spot exchange rate on the Swiss franc is $0.8020/CHF. On July 1, what is the value of your short position you entered on June 1? Assume the forward contract prices are arbitrage free prices.

Answer 1

Arbitrage free pricing:

Forward price ($/CHF) = Spot Price *(1+interest rate in US / 1+interest rate in Switzerland)

As on June 1: (4 months to expiry)

Forward price ($/CHF) = 0.80 * [1+ (0.02*4/12) / 1+ (0.05*4/12) ] = 0.80 * (1.0067/1.0167) = $0.7921/CHF

Now,

As on July 1: (3 months to expiry)

Forward price ($/CHF) = 0.8020 * [(1+ (0.025*3/12) )/ (1+ (0.045*3/12)) ] = $0.7980/CHF

We took a short position of 100000 CHF forward at rate $0.7921/CHF on 1st June, but after a month Forward rate as on 1st July increased to $0.7980/CHF

Value of short position after 1 month = Forward Rate as on June 1 / (1+Interest rate in Switzerland for 3 months) - Forward rate as on July 1 / (1 + interest rate in US for 3 months)

= (0.7921/(1+ (0.045*3/12)) - (0.7980/(1+ (0.025*3/12) ) = 0.7833 - 0.7930 = - $ 0.0097/CHF

Total Loss = 1,00,000 * - $0.0097/CHF = $ 970