Question

QiAption #9 (10 points) For an 8% semiannual coupon bond that has 18 years plus 4 months to maturity, what's the conversion factor? 3

Answer 1

Q1: Conversion factor; The conversion factor of bond is set equal to quoted price bond that have per dollar of principal on the first day of delivery month on the assumption that interest rate of all securities equal to 6% per annum with semiannual compunding.

In this way 8% semiannual coupon bond of 18 years and 4 month to maturity can be calculated as follows:

For calculation of conversion factor th said bond is assumed to have 18 years and 3 month to maturity. The coupon payment is assumed to be paid after 6 month interval till end of maturity.

Discounting all the payments back to a point in time 3 month from today at 6% per annum we can get conersion factoras below:

4+ $\sum i=1 to 36$ 4/1.03i + 100/1.0336 = $125.84

The interest rate for 3 month period is $\sqrt{1.03}$ -1 = 1.4889%

discounting back to value it gives as $125.84/1.04889 = $123.99

We will subtract accrued interest of 2.0 it gives $121.99 and conversion factor is 1.2199.

conversion factor is 1.2199. ans.

Q2: Put Call Parity Derivation:

Put call parity implies equivalence of calls and puts. Parity means put and call can used interchangeabley in portfolio.

• We will derive put call parity relation by creating two portfolio at same payoffs. static replication with rational pricing.
• Consider a call option and put option with same strike price K with same date T on one stock S. We assume a bond that pays 1 dollar at maturity time T. Take random bond price.
• Suppose price of S bond at time T be S(t). We will make active portfolio of buying a call option C and selling a put option P at same maturity T and strike price K.
• The payoffs of this portfolio will be S(t) - K. If we take second portfolio by buying one share and borrowing K bond the payoff for this portfolio will be S(t) - K.
• The following portfolio shows that pay offs for identical have same price.
• thus the below relationship is derived : C(t) - P(t) = S(t) - K
• Which is called as Put call Parity.