Question

The price of Chive Corp. stock will be either $70 or $90 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 6 percent.

  

Suppose the current price of the company's stock is $75. What is the value of the call option if the exercise price is $65 per share? Suppose the exercise price is $85 in requirement 1. What is the value of the call option now?

Answer 1

Answer
CMP as on expiry	Probablity	Expected CMP as on Expiry
90	p	90p
70	1-p	70(1-p)
Therfore	1	90p+70(1-p)
Therefore CMP as on Today=	90p+70(1-p)
		(1+0.06)
	75=	90p+70(1-p)
		(1+0.06)
	75(1+0.06)=	90p+70-70p
	75*1.06=	20p+70
	79.5-70=	20p
	9.5=	20p
	p=	9.5/20
	p=	0.475
Therefore	1-p=	1-0.475
	1-p=	0.525
CMP as on expiry	exercise price	Fair value of call	Probablity	Expected Fair OP
90	65	25	0.475	11.875
70	65	5	0.525	2.625
			=	14.5
Expected Fair OP as on Today=	14.5	=	13.68
		1.06
IF CMP as on Expiry=	85
CMP as on expiry	exercise price	Fair value of call	Probablity	Expected Fair OP
90	85	5	0.475	2.375
70	85	0	0.525	0
			=	2.375
Expected Fair OP as on Today=	2.375	=	2.24
		1.06

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