Questions tagged [libor]
LIBOR was the London Inter-Bank Offered Rate. It has been replaced by The SOFR (Secured Overnight Financing Rate).
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From Libor Curve rates to "forward" zero-coupons
I am provided a 6M euribor curve, constructed from FRA's and swaps of tenor 6M on the euro, as well an EONIA curve, constructed from zero-coupons EONIA swaps. Both curves are provided as functions $d\...
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Building SOFR curve - explanation of the formula used
I am studying a previous post on how to build SOFR discount curve here Libor transition: Building SOFR discount curve
However, I struggle to understand the below ...
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How do forward-looking forward rates in the Mercurio's and Lyashenko's normal or extended FMM model represent EURIBOR rates
(By XIBOR I intend any EURIBOR or LIBOR rate. By RFR I intend SOFR for the USD and ESTR (€STR) for EUR.)
I am mainly focused on the EUR rates market (but also a bit on the USD market) and looking for ...
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Risk free rate for currency option
I’m trying to price a call option on EUR/GBP exchange rate and it expires in 1 year. Should I use GBP Libor as foreign risk free rate in order to apply BS formula? The pricing date is 02/21/2023 but ...
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What are the quantitative models for modelling the SOFR rate, the IR products when Libor rates end [duplicate]
Many year ago, I worked on the pricing of IR products (Floating rate swap, CMS swap, Cap, Floor,...)
Libor rates are now replaced by SOFR rate. I would like to know
What are the new IR products (...
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LIBOR rate used for computing discount margin
A formula for computing the discount margin of a floater is provided in an image displayed in this answer as well as below. The image below comes from page 14 of the paper "Credit Spreads ...
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Relationship between simple Libor spot and forward rates
How is the simple forward rate L(0,T,T+1) calculated given the spot rate L(0,T)?
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Money account discounted libor rate is it a martingale under risk neutral measure?
I see that Libor $L(t,S,T)$ is a martingale under $T-$forward measure. Where we used argument that zero-coupon bonds are martingales under $T$-forward measure, as zero-coupon bond is a traded security....
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SOFR Transition for Future Flow Transactions [duplicate]
I’m looking for some papers/articles for the transition from LIBOR to SOFR for future flow transactions/securitizations (such as Diversified Payment Rights).
Would be happy if you could share some as ...
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Computing Daily OIS overnight trade coupon payments in excel
So I currently work in MO G10 rates sales support and we always get referrals from our setts department to recalculate discrepancy's in vanilla swaps trades coupon payments, this issue is, training ...
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what is the definition of resetting tenor and time to maturity tenor in libor rates
I have a question about the definition and understanding of libor rates. We have the time to maturity tenor, $T$, which is the time over which i borrow or lend money. For libor we also have the reset ...
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What is Dual Curve Bootstrapping? And how to do it, with an example?
I am starting to explore this area. My ultimate aim is to build a 3 month LIBOR forward curve.
I wish to know what exactly 'Dual Curve Bootstrapping' is (If someone could explain it in clear words).
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Libor Market Model Implementation
I'm trying to implement an LMM-MultiCurve for caplet pricing following the analytical formula mentioned in this article (pg 20):
https://www.researchgate.net/publication/...
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Test Log-Normality for LIBOR forward rates under the Libor Market Model
As far as I understand, under the Libor Market Model the forward rates are assumed to have a log-normal distribution. Given that I have constructed my LMM model and now have a matrix of:
k different ...
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Exploding Libor Rates in Libor Market Model
I have implemented the Libor Market Model in Matlab. When I generate a number of paths, I notice that some of them explode. Does anybody have an idea what could cause this?
I already tried solving ...
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Intuition for consistent Derivative Prices under different Numeraires and Measures
This is essentially the Fundamental Theorem, however I am not asking for a thorough proof, I am more interested in the general intuition.
In words, it makes sense that whatever your unit of account (...
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Why is the LMM with mixture dynamics (Brigo & Mercurio) inconsistent for the pricing of exotics?
I am reading about the LMM with lognormal-mixture dynamics. Consider the following dynamics for the forward rate $F_{i}(t)$ fixing at $T_{i-1}$ and paying at $T_i$:
\begin{align}
dF_{i}(t) = (F_i (t) +...
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Why are LMM+ parameters becoming more unstable when using an inverted volatility term structure
I have an implementation of an LMM+ model (a shifted Libor Market Model with rebonato volatility function) and am seeing recently that the calibrated parameters are becoming more unstable over time; I ...
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Rate interpolation in Libor Market Model
Libor Market Model (LMM) models the interest rate market by simulating a set of simply compounded, non-overlapping Libor rates which reset and mature on predefined dates. How do I obtain from them a ...
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Pricing Swaption Analytically using Libor Market Model
I was asked the following question in a recent interview: "(i) Express a forward swap rate in terms of forward Libor rates. (ii) Apply Ito's lemma to this expression to derive the process for the ...
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Libor Market Model definitions in Options, Futures & Other Derivatives, Hull 9th Ed, p744
Re: Options, Futures & Other Derivatives, Hull 9th Ed, p744.
What does "m(t)" represent? I am struggling to understand the definition provided of:
"Index for the next reset date at ...
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Forward starting zero-coupon bonds
We trivially have that:
$$\frac{Z(t_0,t_1)}{Z(t_0,t_2)}=1+\tau L(t_0,t_1,t_2)$$
Where $L(t_0,t_1,t_2)$ is the forward Libor between $t_1$ and $t_2$, as of $t_0$.
Simply inverting this relationship ...
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LMM multifactor swaption calibration
Brigo and Mercurio give Rebonato's approximation for Black-like swaption volatility as
$(v^{LFM}_{\alpha,\beta})^2=\sum^\beta_{i,j=\alpha+1}\frac{w_i(0)w_j(0)F_i(0)F_j(0)p_{i,j}}{S_{\alpha,\beta}(0)^2}...
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Can you shift a standard libor market model with regard to only at-the-money options?
Suppose I have an LMM defined using the spot measure as in Brigo and Mercurio:
$dF_k(t) = \sigma_k(t)F_k(t)\sum^k_{j=\beta(t)}\frac{\tau_j\rho_{j,k}\sigma_j(t)F_j{t}}{1+\tau_jF_k(t)}dt + \sigma_k(t)...
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Using converted lognormal volatilities for negative rates in a lognormal Libor Market Model (LMM)
There exist formulas to convert between normal and lognormal interest rate volatilities. In the most simple form the approximation for ATM volatilities would be $\sigma_{LogNorm}=\frac{\sigma_{Norm}}{\...
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Should the Libor Market Model using spot measure as numeraire simulate an arbitrage free forward curve?
I have been looking at the following resource:
Reference Paper
Using equation [4] for the discretized version of the forward libor rate:
$\tilde{L}^i_{T_{j+1}} = \tilde{L}^i_{T_{j}} exp[\sigma^i(\sum^...
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Replacement for LIBOR Market Model (LMM)?
With the transition from LIBOR to SOFR, will the LIBOR Market Model be replaced by a new model? Perhaps this has already happened. If yes, what is this new model? If not, will the LIBOR Market ...
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Is there an Australian Interbank Rate?
Most widely used Interbank Rates are LIBOR, EURIBOR. Then I read online on SIBOR (Singapore).
It says Canda, US are following LIBOR as well. So for Australia, is there a dedicated interbank rate like ...
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USD Libor fixing rule
I am missing something in the fixing rules for USD Libor: the fixing for the date Aug 31th, 2022 is on Aug 26th, 2022 - 3 ...
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2 Ways to Define/Calculate "FVA"? - Same or Different? (Simple XVA Question)
I've got a very simple question on 2 different ways of defining or calculating the FVA of an uncollateralized swap.
One definition I've often seen is that the FVA is the difference in the net present ...
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What is the market standard for IR option pricing when moving to SOFR
From books it looks like market standards to price IR options, like swaptions, are SABR, LMM or mix of the two (SABR-LMM).
But LMM models the forward LIBOR rate. What will happen to it once LIBOR ...
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Backset LIBOR contract
Below is an extract from Steven Shreve’s BK 2, Chapt 10: Term Structure models. LINK
I am trying to understand Stochastic Calculus from the above book with the help of a Pure Math PhD student.
Despite ...
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Stub rate and first fixing in IRS
I have 2 questions that probably are related.
Suppose there is an IRS that pays a 2% fixed rate every 6 months and receives the Libor 3 months (but paid every 6 months).
The swap starts today (March ...
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Why are Eurodollar futures settled to 100 minus LIBOR? Is this actually connected to a Eurodollar depsoit?
I'm confused as to why Eurodollar futures prices settle to $100-LIBOR$ at expiration. If at the time of settlement the futures contract was meant to represent a 1,000,000 Eurodollar deposit to mature ...
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Is a swap fixed rate always a par yield?
I am learning about using the OIS fixed rate to value a plain vanilla LIBOR swap. I'm using Bond Math by Smith, and the accompanying online addendum.
To bootstrap the discount factors, the author ...
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Pricing caps/floors on backward-looking USD SOFR with forward-looking LIBOR model
The payoff of a cap/floor is calculated as a payoff of constitutient caplets/floorlets.
The SABR volatility model has the implied volatility approximations of Hagan et al.
$$\sigma^f_{IV}\approx \...
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Bloomberg SWPM: Day count to calculate discount factor for US0003M
I'm trying to replicate price I get for CCIRS in SWPM. This is USD3m float vs RUB 1Y. Second leg doesn't matter for my question.
Suppose today is 7th of Jan 2019, deal date. Settlement will happen on ...
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What can be used to replace the Libor - OIS indicator in assessing fear in money markets?
Libor is dead and used to be uncollateralised. Libor-OIS was a useful indicator to measure the spread between risk free (central bank e.g. Fed funds) rate and the interbank lending rate. For example ...
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Why is the fixed leg of a libor swap 30/360 and the floating is actual/360?
I have been looking at the following post (and comparing it to SWPM in Bloomberg)
https://kiandlee.blogspot.com/2021/07/interest-rate-swap-pricing-using-r.html
Why does the fixed leg accrue in 30/360 ...
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Why is USD LIBOR used for USD denominated securities?
I am just starting on Interest Rate Swaps & curve construction. While reading few materials on Interest Rate Swap, it's indicated for e.g. "Floating Coupon Index: 6 month USD LIBOR".
LIBOR is ...
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Floating swap payoff with rate determined on current instead of previous date
I am attempting to determine the payoffs a modified swap, in which the floating payments at a time $T_k$ are made on the current date (i.e. $L(T_k,T_{k+1})\equiv L_{k+1}(T_k)$) rather than at the ...
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DV01 on LIBOR vs. SOFR basis Swaps
If I had entered into a USD 10mn pay SOFR, receive 3M LIBOR swap with a 5yr maturity, I would have had a positive NPV of about 80k by the beginning of March due to the massive drop in SOFR (1.55 to 0....
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LIBOR-in-arrears swap
Let's say we have a situation where all 12-month LIBOR forward rates at 8% per annum with annual compounding. All cap volatilities are 16%. Estimates the difference between the way a sophisticated ...
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Why should the Discount Curve be risk-free?
I have read up about the discount curve that is being used to value securities. The multi-curve methodology for valuing derivatives was mainly adopted because LIBOR was no longer seen as a proxy for ...
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Data for OIS and Libor rates
I want to bootstrap OIS zero-coupon bonds to the OIS rate but unfortunately I don't have any data.
Does anyone know where I can find the Libor rates and OIS rates?
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Day Count Convention
I am currently reading the book Term-Structure Model, chapter 3, by Damir Filipovic and I have the following problem:
The Libor rate for the maturities: Over night, 1 week, 1 month, 2 months and 3 ...
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Currency hedging 3 month sterling libor futures
Each libor contract is 500,000 gbp. Can I hedge it by going short 8 gbp/usd futures per libor to hedge out currency risk considering each gbp/usd futures is 62,500 British pounds?
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How to account for the credit spread ( e.g. LIBOR + 2%) when using the Multicurve Methodology in valuing a Swap
When valuing an Interest rate swap, counterparties will typically issue the contract at a Libor + credit premium, e.g. Libor +2%. When valuing a swap, we require a LIBOR forward curve and Discounting ...
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LIBOR rate and eurodollar futures
If the libor rate stays the same -which implies that also the eurodollar future quoted price remains the same- (ie: jun '22 prices is trading at 99.8, and it expires at 99.8), does the investor that ...
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Using a Swap curve to price Interest rate Swaps
Say we have a 3-m LIBOR IRS (interest rate swap) with quarterly fixed payments (2 year contract), and we want to value this contract (after say 6 months has passed, i.e. there remain 1.5 years to ...
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