SERVING THE QUANTITATIVE FINANCE COMMUNITY

 
User avatar
karfey
Topic Author
Posts: 58
Joined: October 3rd, 2012, 12:37 am

Convexity adjustments in the following IR payoffs

February 18th, 2016, 4:51 am

Hi, I understand the need for convexity adjustments in the following payoffs:-libor-in-arrears-futures when used in curve buildingI understand these adjustments from the angle of "early payment advantage", where an investor has a choice of investing a payment at a higher rate (when he is in receipt), or borrowing at a lower rate (when he is in payment). I shall not go into the martingale measure vs payment measure definition, and will also leave CMS and quanto adjustments out of this discussion for now. Now, how about these set of payoffs:-fixed leg range accrual swap-floating leg range accrual swap (with float = range index)-floating leg range accrual swap (with float <> range index)-zero Coupon Swap ? No Compounding-zero Coupon Swap ? With CompoundingCan anyone share with me their thoughts on the 5 payoffs above--whether convexity adjustments are necessary?Thanks!
 
User avatar
bearish
Posts: 5697
Joined: February 3rd, 2011, 2:19 pm

Convexity adjustments in the following IR payoffs

February 18th, 2016, 11:18 am

The zero coupon swap with compounding sounds like the only candidate for not needing "a convexity adjustment", or somewhat more generally valuation through a dynamic interest rate model. The only class of fixed income instruments that can be valued by simple discounting is comprised of those that can be expressed as a portfolio of zero coupon bonds, so it's the old story of dividing the universe into bananas and non-bananas. And that is before entering into the multi-curve world...
 
User avatar
karfey
Topic Author
Posts: 58
Joined: October 3rd, 2012, 12:37 am

Convexity adjustments in the following IR payoffs

February 19th, 2016, 5:15 am

appreciate your ever-present replies.Btw, I thought the multi-curve world will not add any more complexity, other than an upfront deterministic spread on a base curve (usually libor) to denote the multi-curves?So convexity adjustment issue will no longer be relevant for Range accruals if we use models like HW 1F?
 
User avatar
bearish
Posts: 5697
Joined: February 3rd, 2011, 2:19 pm

Convexity adjustments in the following IR payoffs

February 20th, 2016, 12:43 am

In terms of the last question, no - as long as you use an internally consistent model to generate both the cash flows and the relevant pathwise discount factor, no further adjustments are required. The multi-curve world is murky as far as I am concerned, but given that it breaks the telescoping argument that lets you value a Libor leg by simple discounting, I am afraid that you need to rely on weaker arguments (like a deterministic basis between curves) to do model free valuation. But, honestly, I moved on to do other things by the time this became really important...
 
User avatar
prodiptag
Posts: 124
Joined: September 12th, 2008, 4:41 pm

Convexity adjustments in the following IR payoffs

March 10th, 2016, 8:42 pm

To best of my knowledge-fixed leg range accrual swap: no-floating leg range accrual swap (with float = range index): no-floating leg range accrual swap (with float <> range index): ?-zero Coupon Swap ? No Compounding: yes-zero Coupon Swap ? With Compounding: noin all cases except 4 you have matching numeraire, - the range accruals can be replicated with digitals (for fixed) or caplet spread (for floating), no adjustment as long as these are traded assets, the zero coupons with compounding is also natural. Only case you need is there is a mismatch which is the case 4. I do not understand what you mean by float <> range index
ABOUT WILMOTT

PW by JB

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...


Twitter LinkedIn Instagram

JOBS BOARD

JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...


GZIP: On