Question

An analyst is interested to value put options on the stock of Bulls Inc. The analyst has accumulated the following information:

• The price of the stock is $40. • The strike price is $38. • The option matures in 2 months. • The variance of the stock’s returns is 0.25. • The annual risk-free rate is 6%.

Using the Black-Scholes model, what is the value of the put option?

Answer 1

	Option price=	= Xe –rt × N(-d2) – S × N(-d1)
	d1 =	[ ln(S/X) + ( r+ v2 /2) t ]/ v t0.5
	d2 =	d1 - v t0.5
	Where
S=	Current stock price=	40
X=	Exercise price=	38
r=	Risk free interest rate=	6%
v=	Standard devriation=0.25^1/2=	50%
t=	time to expiration (in years)=	2/12 =	0.166667
d1 =	[ ln(40/38) + ( 0.06 + (0.5^2)/2 ) *0.16667] / [0.5*0.16667^ 0.5 ]
d1 =	[ 0.05129 + 0.0308333333333333 ] /0.204124
d1 =	0.4023367
d2 =	0.40234 - 0.5 * 0.16667^0.5
	0.198212519
N(-d1) =	N( - 0.40234 ) =	0.34372
N(-d2) =	N( - 0.19821 ) =	0.42144
	38 × e^(-0.06 × 0.16667) ×(1- N( 0.19821)) -40× (1-N(0.40234))
Option price=	2.11

Put price is $2.11

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