Question

The current price of $1 par of a zero maturing at time 2 is $0.90. In addition, you can
contract today to purchase, at time 2, $1 par of a zero maturing at time 3. The forward
price to pay at time 2 for this zero maturing at time 3 is $0.94. It costs nothing today
to enter into this forward contract.
a)
What is the forward rate from time 2 to time 3?
b)
Describe transactions in the 2-year zero and the forward contract that together
synthesize a spot purchase of $1 par of the zero maturing at time 3. (With the spot
purchase, you pay for the zero today, rather than in 2 years.)
c)
Assuming there are no arbitrage opportunities, what is the current spot price (the
price to pay today) for $1 par of the zero maturing at time 3?

Answer 1

	Forward rate from time 2 to 3:
	Par valiue	$1
	Purchase price at time 2	$0.94
	Forward Rate=r
	0.94*(1+r)=`1
	1+r=1/0.94=	1.0638
	r=	0.06383
	Forward rate from time 2 to 3:	6.38%
	2 year 0 at time 0 willmature in time 2
	Forward contract fromtime2 to3 will mature in time 3
	Synthesis of the above two will be equivalent to ourchase of 3 year 0
	1.Purchase 2 year 0 at spot price
	2. Purchase one year forward at time2
	3. After maturity of 2 year 0at time 2, pay for the one year 0 at time 2
	Price of $1par zero maturing at time 3
	Forward rate r for zero at time 2 maturing in time3	0.06383
	Rate of 2 year zero maturig at time2=r1
	$90*((1+r1)=$1
	(1+r1)=1/0.90=	1.1111111
	r1=Rate of 2 year 0 at time 0	0.1111111
	Assume Rate of 3 year zero=R
	1+R=(1+r1)*(1+r)
	1+R=1.111111*1.06383=	1.1820
	R= Rate of 3 year 0	0.18
	Price of $1par zero maturing at time 3=1/(1+R)=	0.85
	Price of $1par zero maturing at time 3	$0.85