Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Rational pricing
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==Fixed income securities== :''See also [[Fixed income arbitrage]]; [[Bond credit rating]].'' Rational pricing is one approach used in pricing [[fixed rate bond]]s. Here, each cash flow on the bond can be matched by trading in either (a) some multiple of a [[zero-coupon bond]], ZCB, corresponding to each 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 [[Zero-coupon bond#Strip bonds|strip]] corresponding to each coupon, and a ZCB for the return of principle on maturity. Then, 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 (per {{slink|#Assets with identical cash flows}}). Were this not the case, arbitrage would be possible and would bring the price back into line with the price based on ZCBs. The mechanics are as follows. Where the price of the bond is misaligned with the present value of the ZCBs, the arbitrageur could: # finance her purchase of whichever of the bond or the sum of the ZCBs was cheaper # by [[short selling]] the other # and meeting her cash flow commitments using the coupons or maturing zeroes as appropriate # then, her profit would be the difference between the two values. The pricing formula is then <math> P_0 = \sum_{t=1}^T\frac{C_t}{(1+r_t)^t}</math>, where each cash flow <math>C_t\,</math> is discounted at the rate <math>r_t\,</math> that matches the coupon date. Often, the formula is expressed as <math> P_0 = \sum_{t=1}^ T C(t) \times P(t)</math>, using prices instead of rates, as prices are more readily available. ===Yield curve modeling=== Per the logic outlined, rational pricing applies also to interest rate modeling more generally. Here, ''[[yield curves]]'' in entirety must be arbitrage-free [[Yield curve#Construction of the full yield curve from market data|with respect to the prices of individual instruments]]. Were this not the case, the ZCBs implied by the curve would result in quoted bond-prices, e.g., differing from those observed in the market, presenting an arbitrage opportunity. [[Investment banks]], and other [[market maker]]s here, thus invest [[Quantitative_analysis_(finance)#Front_office_quantitative_analyst|considerable resources]] in "curve stripping". See [[Bootstrapping (finance)]] and [[Multi-curve framework]] for the methods employed, and [[Model risk]] for further discussion.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)