Fixed Income Securities
Rational pricing is one approach used in pricing fixed rate bonds. Here, each cash flow can be matched by trading in (a) some multiple of a zero-coupon bond corresponding to the coupon date, and of equivalent credit worthiness (if possible, from the same issuer as the bond being valued) with the corresponding maturity, or (b) in a corresponding strip and ZCB.
Given that the cash flows can be replicated, the price of the bond must today equal the sum of each of its cash flows discounted at the same rate as each ZCB, as above. Were this not the case, arbitrage would be possible and would bring the price back into line with the price based on ZCBs; see Bond valuation: Arbitrage-free pricing approach
The pricing formula is as below, where each cash flow is discounted at the rate that matches the coupon date:
- Price =
Often, the formula is expressed as, using prices instead of rates, as prices are more readily available.
See also Fixed income arbitrage; Bond credit rating.
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