Question

Suppose Ford's stock price is currently $10, and in the next six months it will either fall to $8 or rise to $15. The six-month risk-free interest rate is 1% (it is not the yearly rate). What is the current value of a six-month call option with an exercise price of $10? Explain your answer.

Note: std of the u and d are not needed...

Answer 1

Solution:
	Spot price	10
	6 months downward price	8
	6 months upward price	15
	6 months Risk free rate,r	1%
	Exercise price	10
	If price moves up	15
	If price moves down	8
	u	1.5	=15/10
	d	0.8	=8/10
	Probability of up movement	0.30	=1+r-d/(u-d)
			=(1+1%-0.8)/(1.5-0.8)
	Probability of down movement	0.70	=1-0.30
	Value of the Call Option using the binomial model	1	=((Probability of upward movement*Upward price)+(Probability of downward movement*Downward price))/1+r
			=((0.30*1.5)+(0.70*0.8))/1.01