Question

Find the dollar value today of a 1-period at-the-money call option on €10,000. The spot exchange rate is €1.00 = $1.25. In the next period, the euro can increase in dollar value to $2.00 or decrease to $0.80. The risk free rate in dollars is i_$ = 17.60%; the risk free rate in euro is i_€ = 5.00%

Answer 1

Now P = Probability of up move

p = (R -d ) / (U -d)

Where R is the risk free rate

d is the downward movement

U is the upward movement

U = 2/ 1.25 =1.6

d = 0.8/1.25 = 0.64

p = ( 1.05 - 0.64) / ( 1.6 - 0.64)

= 0.41 / 0.96

= 42.71%

1-p = 1 -0.4271 = 57.29%

Call value after 1 period in upmove = Max ( Stock prie - strike price,0)

= Max ( 20000 - 10000 , 0)

= 10000

Call value after 1 year in downward move = 0 as the exchange rat eis lower than the strike price

So dollar value today = (10000 * 0.4271 + 0 *.5729) /1.05

= 4271 /1.05

= $4067.62