Question

1. You purchase an interest rate futures contract that has an initial margin requirement of 9% and a futures price of $130,538. The contract has a $100,000 underlying par value bond. If the futures price falls to $126,500, you will experience a ______ loss on your money invested.

Multiple Choice

A 24.00%

B 57.37%

C 45.37%

D 34.37%

2. Malmentier SA stock is currently priced at $120, and it does not pay dividends. The instantaneous risk-free rate of return is 7%. 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 $125 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.

A 21

B 25

C 60

D65

Answer 1

1

Particulars	Amount
Decline in value	4038
/ Investment	11748.42
Return on investment	34.37%

2

	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=	120.00
X=	Exercise price=	125
r=	Risk free interest rate=	7%
v=	Standard devriation=	40%
t=	time to expiration (in years)=	1/12 =	0.083333
d1 =	[ ln(120/125) + ( 0.07 + (0.4^2)/2 ) *0.08333] / [0.4*0.08333^ 0.5 ]
d1 =	[ -0.04082 + 0.0125 ] /0.11547
d1 =	-0.2452757
d2 =	-0.24528 - 0.4 * 0.08333^0.5
	-0.360745721
N(-d1) =	N( - -0.24528 ) =	0.59688
N(-d2) =	N( - -0.36075 ) =	0.64086
	125 × e^(-0.07 × 0.08333) ×(1- N( -0.36075)) -120× (1-N(-0.24528))
Option price=	8.02

N(d1) is 0.59688

Hedge ratio = 100 * 0.59688 = 60

Answer is:

60