# Tag Info

12

It comes down to the definition of LIBOR: London Interbank Offer Rate -> Every business day, a panel of large banks are asked by the BBA[*] (British Bankers Association) at what rate they would lend cash (unsecured) in a certain currency to another bank of that panel for a certain maturity, and that for a range of currencies and maturities. e.g. Currency: ...

10

Let us denote $\delta$, the Libor's tenor (e.g. 3M), $P(t, T)$ the price of a zero coupon bond price paying 1 unit of currency at $T$, and $L_t(T, T + \delta)$ the forward 3M Libor starting at $T$ and ending at $T+\delta$, seen from $t$: $$L_0(T, T + \delta) = \frac{1}{\delta} \left(\frac{P(0, T)}{P(0, T + \delta)} - 1 \right)$$ The vanilla case: payment at ...

9

Why does USD based security valuation have to give a thing about what London Banks think? Your question is based on false premises: the USD Libor is not determined by polling London based banks as you seem to believe, but banks on the London money market. The difference is important, as there are—of course—banks which are not based in London and active on ...

8

Firstly, understand that the 1y Libor is not useful here; the swap is 2 6-month periods, which will each fix on 6m Libor. These days, the *ibor fixings at different tenors are essentially separate, and 0x6 & 6x12 do not compound up to 0x12. So we have 6m fixing at 0.63006%, and a 1y swap at 0.645% mid. To do this properly, we would need a discounting ...

8

The market is using SOFR discounting for all sorts of quotations already (not FF). For example, swaption vol is quoted with SOFR discounting, CME and LCH moved to SOFR PAI and discounting on Oct. 16 2020 on new AND legacy swaps. For EUR cleared, major CCPs did this since July 27 2020. The market switched to discounting with the relevant RFR rates on the ...

6

Federal Home Loan Banks also hold reserves, but are not eligible to earn IOER, so they lend the cash into the fed funds market at a rate below IOER. U.S. branches of foreign banks, who are eligible to earn IOER, borrow from the FHLBs and deposit the proceeds in their accounts at the Fed, earning the spread. U.S. banks don't participate in this arbitrage ...

6

First point to consider : some banks are by nature "positive" in their account to the central banks , for instance classical saving banks tend to get more deposit than loans; conversely others are more engage in loans activity (investments banks..) and are by "nature" borrowers on Interbank markets. Secondly (the point you underestimate), mandatory ...

6

Better yet, don't use LIBOR for discounting at all. Since LIBOR involves credit spread over the risk free rate, using LIBOR for discounting would adjust the deal's market value to reflect some amount of credit risk. Hull and White argue it's not generally the best idea, since it would mean double-counting, as one also normally computes the CVA to handle ...

6

It is not reasonable because rates display a stationarity but brownian motion is not stationary. The variance of libor at a future time $t>0$ conditional on the value at time $t=0$ does not scale as $\sqrt{t}$

6

A multi-curve meants that you observe the discounting instruments (such as fed funds) and projection (libor, swap curve) and solve for all of them simultaneously; as opposed to bootstrapping separately a projection curve and a discounting curve. A simple paper with examples is Numerix Model Calibration: The Multiple Curve Approach. A more detailed intro is ...

5

The importance here is that it actually does not matter in what time zone or market the libor rates are set. Key is that it is supposed (!!!) to be a gauge at what rate contributing banks could borrow funds at in the inter-bank market. Like you can go to any African country and borrow or lend US dollar, so can any Japanese, European, or American bank borrow ...

5

EDIT: I changed the answer to have it more on topic. Summary It boils down to Mark Joshi's answer. I wanted to add something more. Answer A probability measure $Q1$ and a numeraire $N1(t)$ are associated if all prices expressed relative to $N1$ are martingales under $Q1$: \frac{price(t)}{N1(t)} = \mathbb{E}^{Q1} \left[ \left. \frac{price(T)}{N1(T)} \, ... 5 this is a well-known problem. One solution is to make volatility zero when rates exceed a certain high level. It's less problematic than it looks because any cash-flows generated will be divided by a rolling money market account which has huge value and so the deflated cash-flows are very small. 5 Good questions! Libor is indeed specific to London, Tibor is specific to Tokyo. In New York banks lend to each other overnight in the Federal Funds market (confusingly, the Fed is not a counterparty to those trades; they are overnight interbank trades). The interest rate swap market started in London in the 1980s , and spread worldwide. As it spread, ... 5 A 3 month libor curve is a set of forward rates for 3 month libor. Thus, the curve begins at where 3 month libor is today , and takes different values for each possible forward observation date. Loosely speaking, this curve represents where the market thinks 3 month libor will set in the future. The analogous statement holds for 1mo libor , 6 month ... 5 You use the curve that describes the floating rate index to estimate the floating rate cashflows, a swap against floating 3M uses a 3M curve to forecast the cashflows. And then you use a discounting curve to discount the future cashflows that aligns with the funding/collateralisation of the derivative. For example almost all cleared swaps will use the OIS ... 5 RFR (risk free rate) is the current acronym ISDA, central banks and regulators are pursuing to signify and politicise the transition from IBOR, which has been dogged by rigging scandals. OIS (overnight index swap) is the acronym that has been associated with an unsecured overnight interbank cash lending rate fixing (OIS fixing) (with different calculation ... 5 Two replacements for the 3M Libor curve are possible: Construct a new 3M Swap discounting curve by adding spreads on top of the SOFR curve. These spreads can be calibrated on uncollateralized 3M SOFR swaps. Discount all derivatives, regardless if collateralized or not, with the SOFR curve, which is the true risk free curve. The credit risk arising from not ... 4 Libor rates include credit risk. It is riskier to make a 6m loan than two 3m loan. So the 6M Libor curve is not the same as the 3M one. Their difference is the basis spread. When using a short rate model, you are modelling one curve. As a first approximation, you can deduce the other curves by adding a deterministic basis spread. 4 The flaw is L(T,S) is a future spot rate that is determined at time T>t and unknown at present. It is correct thatF(t,T,S)=\frac{1}{S-T}\left[\frac{P(t,T)}{P(t,S)}-1\right] \iff P(t,S)(S-T)F(t,T,S) = P(t,T) - P(t,S), $$as this is just the definition of the forward rate. However, you are saying that$$\frac1{P(t,T)}\frac1{P(T,S)}=\frac1{P(t,...

4

I think to have the answer: use qlBondPreviousCashFlowDate() pointing at your FloatingRateBond object to get the last date of payment; use qlInterestRateIndexFixingDate() to get the fixing date referring to the last payment date; use qlIndexAddFixings() to add a fixing rate to the fixing date you got above; repeat for each one of your bonds if they share ...

4

An OIS, or Overnight Index Swap, is an interest rate swap whose floating leg payments are calculated as a geometric average of the daily fixings of some underlying O/N or T/N index (these indices are generally volume-weighted averages of reported daily transactions). The annualized floating leg rate is defined as $$c_T^{float} = \frac{\prod^{s+T}_{t=s}{(1+... 4 No, you can't. You can never deduce the 3M/6M basis spread from 3 month instruments alone. If you consider the OIS curve riskless, you can interpret the 3 month curve as riskless rate + additional cost for things like credit risk, liquidity and so on. The 6 month rate contains even more of these credit risk and liquidity cost. How much exactly though is ... 4 Many major currencies/money markets have both an onshore money market and an offshore market. London is the offshore market for the USA. All major US banks have a branch in London. Historically this offshore market developed to escape US domestic regulations in the 1960's, but it still survives and even thrives, despite major changes (for example the volume ... 4 There are a lot of intricacies involved, and I'll focus on high-level stuff. Let's go back to the basics. If we have the 3-month LIBOR rate and the 6-month LIBOR rate, can we calculate the 3-month forward 3-month LIBOR rate? Before the financial crisis, the answer was typically assumed to be yes. The math is simple:$$\left(1 + \frac{\text{3-month LIBOR}}{...

4

Collateralised means that when the IRS is negatively valued (i.e. a liability) for one of the counterparties then they post collateral to the other respective counterparty (i.e. the asset holder) to protect them against default of the liability owner. Collateral comes in many forms. The 'gold standard' is cash remunerated at the OIS rate, but it could be ...

4

Interest rate derivative trading relies on curves. The LIBOR rate, be it 1month, 3month, 6month etc is published and determined every day but derivative contracts continue to speculate on what futures day's LIBOR publications will be. A 6M Libor curve does one thing and one thing only. It estimates what 6M Libor will be on any future date. I.e you can '...

4

These total return swaps are basically funding trades. The seller of total return is putting the risk on their balance sheet. In order to pay the total return to the buyer of total return, the seller would need to hedge their risk by buying the risk of the asset. If effect, the total return seller is lending the total return buyer the funds to gain the ...

4

IBOR (Interbank Offered Rate) and OIS (Overnight Index Swap) are two fundamentally different forms of published interest rates. IBOR is calculated as an average of interest rate submissions from a series of panel banks, ignoring upper and lower outliers to improve robustness, and OIS is calculated as a weighted average of executed traded volume in an ...

4

Consider a date sequence \begin{align*} 0 \leq t_0 \leq T_s < T_e < T_p, \end{align*} where $t_0$ is the valuation date, $T_s$ is the Libor start date, $T_e$ is the Libor end date, and $T_p$ is the payment date. Let $\Delta_s^e = T_e-T_s$. For $0\le t \le T_s$, define \begin{align*} L^e(t, T_s, T_e) = \frac{1}{\Delta_s^e}\bigg(\frac{P(t, T_s)}{P(t, T_e)...

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