I'm reading the book 'Options, Futures and Other derivatives' an having a hard time to understand Conversion factor and CTD bond.
- Conversion factor
I understand this as a factor to adjust the price of the bond delivered to the hypothetical bond(with yield = 6% in my case)
ex. maturity = 20 years. Coupon rate = 10% with semiannual payment. Face value = $100
then in the book, after discounting future cash flow with annual rate = 6%
$\sum_{i=1}^{40} \dfrac5{1.03^i} +\dfrac{100}{1.03^{40}} = $146.23
author says conversion factor is $\dfrac{$146.23}{$100}$ = 1.4623
(If I'm wrong, please tell me. )
I wonder why we deal with only yield. I think the calculation must reflect the difference in maturities of each bonds.
- CTD Bond.
In the book, author said 'when bond yields are in excess of 6%, the conversion factor system tends to favor the delivery of low-coupon, long-maturity bonds.'
I think, this means that under that circumstance, conversion factor increases as coupon rate decreases and maturity increases. However, I can't show that mathematically. I guess I misunderstood or there must be more variables that needs to be considered from the words 'tends to'. How can I understand that description both intuitively and mathematically.