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

We need to calculate the probability of the up move and down move

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

R is the risk free rate = 5%

d = downward movement = 0.8/1.25 = 0.64

u = upward movement = 2/1.25 = 1.60

p = (1.05 - 0.64) / ( 1.60 - 0.64)

= 0.41/ 0.96

= 42.71%

1- p = 57.29%

Payoff in the upward movement = Max ( Spot - Strike , 0)

= Max ( 2 - 1.25 , 0) *10000

= 7500 euros

Payoff in the downward movement = Max ( 0.8 - 1.25 ,0)

= 0

Expected payoff = p * 7500 + ( 1- p)*0

= .4271 * 7500 + .5729 * 0

= 3203.125

Value of the call option = 3203.125 / 1.05 =$3050.595