FRM Fun 3

Discussion in 'Today's Daily Questions' started by Suzanne Evans, Jul 4, 2012.

  1. Suzanne Evans

    Suzanne Evans Administrator

    FRM Fun 3.

    In recent days, a scandal has roiled around LIBOR (e.g., yesterday from @moorehn at, the interest rate used to signify the risk-free rate in many financial texts. Assuming the scandal taints LIBOR, the question is: do we need a risk-free rate in financial analysis (e.g., modeling, valuation, risk measurement) and, if we do need to assume a risk-free interest rate, what is the best alternative to LIBOR?

    (no multiple choice here, just a star for the best given answer!)
  2. Aleksander Hansen

    Aleksander Hansen Well-Known Member

    Overnight Index Swaps (OIS) is currently being used by most banks, hedge funds and investment companies as a risk-free rate.
    That is, whereas the, e.g. 3m LIBOR is still used to project the forward rate [if stipulated by the contract that 3m LIBOR is the index]. Thus, we end up with an interesting phenomena, called dual-curve stripping. That is, given, e.g. a Fixed-Floating swap, the floating rate used to price the future cash-flow is the LIBOR curve, however, the curve used to discount this to PV is the OIS, hence the name, dual-curve stripping. The interesting part about this is that it leads to a non-zero value for the swap at inception! It will generally be close, but not zero: if you want to force it to zero you need to explicitly solve for a zero premium using, e.g., a spread over/under LIBOR on one of the legs.

    Now, as to the question do we need a risk-free rate, I think the answer is no. Let me rephrase, I know the answer is no, because we have never had a truly risk-free interest rate. Would it be nice to have - sure! What is immensely useful though, is a rate that we can consider to be close to risk-free. It should have certain properties, such that, e.g. there is no re-investment risk and so forth.

    The OIS satisfies this and many other desirable properties, and has thus, become the de-facto risk-free rate used. Importantly, unlike the LIBOR and LIBID, there is no submission of rates you 'think' you can borrow or lend at. It is governed by the market, that is, the price-system, and thus ensures efficient allocation of resources.

    Can we find a better rate? Most certainly, and a lot of bright minds are currently working on this.
    • Like Like x 2
  3. PL

    PL Active Member

    Hello Alex,

    The use of OIS as discount factor - i think - comes from the fact that most of the OTC transactions are fully covered under the CSA (daily exchange of collateral). From my point of view we should use different discount factor in cases of no collaterilized transactions versus transactions under CSA.
    What is your opinion?

    Congrats to your success in the exams and i wish you the best in the future plans (wedding - company etc)
  4. Aleksander Hansen

    Aleksander Hansen Well-Known Member

    Actually, in my experience, a typical OTC is not necessarily covered by a CSA, indeed, they are often shunned, so no exchange of collateral actually takes place, but there is an ISDA and credit support annex, with agreed upon collateral [but not exchanged less deault on contact].

    Now, comparing a CSA vs a non-CSA (with no loss of generality), the appropriate discount curve would still be the risk-free OIS in my opinion. Any 'excess' risk should be built into the payments in form of a higher rate or a spread over a floating index.

    Thanks, and congrats to you too on passing!
    • Like Like x 1
  5. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    Aleks, thank you, that is a winning and HELPFUL reply (i.e., you are entered in the weekly drawing)! From my notes (this didn't have a correct answer but my prep happens to comport with your view and frankly you have a better realistic perspective) :
    • John Hull section 4.1. (emphasis mine): "The credit crisis that started in 2007 caused many derivatives dealers to critically review their practices. This is because banks became very reluctant to lend to each other during the crisis and LIBOR rates soared. Many dealers have now switched to using the overnight indexed swap (OIS) rate as a proxy for the risk-free rate. This rate will be explained in Section 7.8. It is closer to the risk-free rate than LIBOR"
    • A short article by CFA Institute that concludes "there is no such thing as a risk-free rate of return" at
    • More technical presentation on OIS at the expert blog xenomorph:; e.g., "The credit crisis of 2007 brought the usage of LIBOR and LIBOR swap rates for discounting purposes into acute focus, as LIBOR spreads to US Treasury rates dramatically increased from the then typical levels of around 50bp to a peak of 450bp in October 2007. This has led many practitioners to now use Overnight Indexed Swap (OIS) rates as a proxy for risk-free rates in derivatives valuation.
    • Like Like x 2
  6. caramel

    caramel Member

    • Like Like x 4
  7. Aleksander Hansen

    Aleksander Hansen Well-Known Member

    Thanks for posting this, I had actually been looking for something more than just a few paragraphs on the topic by a respected authority to reference when using it in my work, so this was just what I needed for documentation purposes!
  8. PL

    PL Active Member

    Thanks a lot
    Great addition
  9. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    @caramel: thank you for sharing this Hull paper, I just read and this is the best summary I've read on the LIBOR-OIS topic (I entered you into the weekly drawing, fwiw. Gold star share :) ).

    Some helpful explain on the OIS (emphasis mine) in the pape:
  10. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    FYI, blog today from soberlook on this:
    --link: soberlook 8/13
    • Like Like x 1
  11. Aleksander Hansen

    Aleksander Hansen Well-Known Member

    I agree with everything but the part about interest on collateral posted with another Counterparty is the fed funds rate. That is too general to hold true. A necessary and sufficient condition would be that the trade is entered into by investors on the margin. However that is not always the case for OTCs.
    A sufficient condition would also be that the margin in the projection of rates that informs future CFs (not the discounting) reflects this.
    • Like Like x 1
  12. bhar

    bhar Active Member

    Hi All. Just to add, there are poll results that indicate that the minds of investors and market players is to move from LIBOR to the Overnight Index Rate. So this could be the future Risk free rate while valuing Swaps. However, the concept of 'Risk free rate' will not be 'eradicated', if I may say so, from the minds of market players. IT would be simply replaced with a non-manipulative one.

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