# Futures Contract and Zero-coupon Bond Rate

2.24

When the money ($1000-($3000-$2000)) lost from one contract, margin call will be have. This could happen when the price of the wheat increase by (1000/ 5000) =$0.2 the price of wheat must increase to (4.5+0.2) = $4.7 per bushel for there to be a margin call. $1,500 can be withdraw from the margin account, this will happen if the futures price fall to (1, 500 / 5,000) = $0.3 to (4.5 – 0.3) $42 per bushel.

4.25

(a)

the six-month zero-coupon bond rate is calculated as follows: Rm=[m*(FV-PV)]/PV

Rm=[2*(100-98)]/98=0.0482

Then this is converted into a continuously compounding rate: Rc=m*ln(1+Rm/m)

Rc=2*ln(1+0.0482/2)=0.04763

The 1 year zero-coupon bond rate is calculated as follows:

Rm=[1*(100-95)]/95=0.05263

Then this is converted into a continuously compounding rate: Rc=1*ln(1+0.05263/1)=0.05129 The 1.5 year zero-coupon bond rate is calculated as follows:

The 2.0 year zero-coupon bond rate can be calculated as follows:

(b)

the forward rates can be calculated as follows:

For instance, the 1F2 rate is calculated:

0.5-1 year:

1-1.5 years:

1.5-2.0 years:

(c)

c=(100-100d)m/A 100=Ac/m+100d

6-months, the par yield of the bond:

M=2, d=e-0.04763*0.5=0.9765, A=e-0.04763*0.5=0.9765

12-months, the par yield of the bond:

M=2, d= d=e-0.05129*1.0 =0.9500, A= e-o.o4763*0.5+ e-0.05129*1.0=1.9265

18-months, the par yield of the bond:

M=2, d= d=e-0.05436*1.5 =0.92595, A= e-o.o4763*0.5+ e-0.05129*1.0+ e-0.05436*1.5=2.8482

24-months, the par yield of the bond:

M=2, d= d=e-0.058009*2.0 =0.8905, A= e-o.o4763*0.5+ e-0.05129*1.0+ e-0.05436*1.5+ e-0.058009*2.0=3.7386

(d)

C=100*7%/2=3.5

Price of bond:

The bond yield is given by solving for y.

=>Y= 0.0577=5.77%

5.23

(a)

the present value of the dividend, I, is given by:

I= 1*e-0.08*2/12+1*e-0.08*5/12=1.95397...

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