Question

Malmentier SA stock is currently priced at $55, and it does not pay dividends. The instantaneous risk-free rate of return is 5%. The instantaneous standard deviation of Malmentier SA stock is 40%. You want to purchase a put option on this stock with an exercise price of $60 and an expiration date 30 days from now. According to the Black-Scholes OPM, you should hold __________ shares of stock per 100 put options to hedge your risk.

• 36

• 40

• 75

• 80

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=	55.00
X=	Exercise price=	60
r=	Risk free interest rate=	5%
v=	Standard devriation=	40%
t=	time to expiration (in years)=	1/12 =	0.083333
d1 =	[ ln(55/60) + ( 0.05 + (0.4^2)/2 ) *0.08333] / [0.4*0.08333^ 0.5 ]
d1 =	[ -0.08701 + 0.0108333333333333 ] /0.11547
d1 =	-0.6597212
d2 =	-0.65972 - 0.4 * 0.08333^0.5
	-0.775191264
N(-d1) =	N( - -0.65972 ) =	0.74528
N(-d2) =	N( - -0.77519 ) =	0.78089
	60 × e^(-0.05 × 0.08333) ×(1- N( -0.77519)) -55× (1-N(-0.65972))
Option price=	5.67

N(d1) is 0.75

Hedge ratio = 100 shares * 75 = 75

Answer is:

75