Question

The current price of a stock is $50. In 1 year, the price will be either $65 or $35. The annual risk-free rate is 10%. Find the price of a call option on the stock that has an exercise price of $55 and that expires in 1 year. (Hint: Use daily compounding.)

Answer 1

Risk neutral probability = [(1+r)^n - d] / u-d

d = 35 / 50

= 0.7

u = 65 /50

= 1.30

= [ (1+0.000274)^365 - 0.7 / [ 1.30 - 0.7 ]

= [ 1.1052 - 0.7 ] / [ 1.3 - 0.7 ]

= 0.4052 / 0.6

= 0.6753

Expected Price	Strike Price	Exercised/ Not	Vc	Prob	Expected Vc	PVF @10%	Vc Today
$   65.00	$   55.00	Exerceisred	$   10.00	0.6753	$     6.75	0.9048	$     6.11
$   35.00	$   55.00	Not Exercised	$          -	0.3247	$          -	0.9048	$          -
Value of Call Today	$     6.11

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