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)

where R is the risk free rate

d= the downward movement value

u = upward movement value

u = 2/1.25 = 1.6

d = 0.80 / 1.25 = 0.64

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

= ( 0.41 / 0.96

= 0.4271

1 - p= 1 - 0.4271 = 0.5729

payoff in the upward movement = Max ( Spot - strike, 0)

= (2 -1.25) *10000 = 7500

payoff in downward movement = 0 as the spot rate is lower than the strike rate

expected payoff = 7500 *.4271 + 0 *.5729

= $3203.25

value of call option = 3203.25 /1.05 = $3050.714