Question

The current spot price is S0= $1.12/€, the volatility of the exchange rate is ? = 9.682%. For a 125 days call option with Strike price = $1.15/€, what is the fair option premium by using binomial option-pricing model? Assume prevailing forward rate F125?day = $1.1245/€, USD interest rate for 125 days is r$ = 2%. Euler’s e = 2.71.

A. $0.2183/€

B. $0.1359/€

C. $0.0768/€

D. $0.0179/€

(Think what if it’s a put option?)

How do you get the answer?

Answer 1

By use of binomial model with 2 steps the

At each node:
Upper value = Underlying Asset Price
Lower value = Option Price
Values in red are a result of early exercise.
Strike price = 1.15
Discount factor per step = 0.9965
Time step, dt = 0.1736 years, 63.37 days
Growth factor per step, a = 1.0035
Probability of up move, p = 0.5330
Up step size, u = 1.0412
Down step size, d = 0.9605

Structure formed will be , below

The risk-neutral probability for the price

P = e^rt -d / (U-d)

		Exchange Rate ($ / foreign):	1.1200
		Volatility (% per year):	9.68%
		Risk-Free Rate (% per year):	2.00%

	Time to Exercise:	0.3472
	Exercise Price:	1.1500
	Tree Steps:	2

Price:	0.04012967
Delta (per $):	-0.623259