Question

The current exchange rate is 0.70472 euros per dollar. The continuously compounded risk-free interest rate for dollars and for euros are equal at 4%. An n-month dollar-denominated European call option has a strike price of $1.50 and a premium of $0.0794. An n-month dollar-denominated European put option on one euro has a strike price of $1.50 and a premium of $0.1596. Calculate n

Formulas would be greatly appreciated

Answer 1

Sol:

Current exchange rate = 0.70472 euros per dollar

Risk-free interest rate for dollars and for euros = 4%

n-month dollar-denominated European call option has a strike price of $1.50 and a premium of $0.0794

n-month dollar-denominated European put option on one euro has a strike price of $1.50 and a premium of $0.1596

To determine n

From put call parity,

Asset + PUT = CALL + Bond

=>1 / 0.70472 + 0.1596 = 0.0794 + 1.5 *e^(-n*4% / 12)

=>1.5786 - 0.0794 = 1.5 *e^(-n*4%/12)

=> 1.49920329 = 1.5 *e^(-n*4%/12)

=> e^(-n*4%/12) = 1

=> n = 0

Therefore the prices are at expiry.

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