Skip to main content

Questions tagged [libor]

LIBOR was the London Inter-Bank Offered Rate. It has been replaced by The SOFR (Secured Overnight Financing Rate).

Filter by
Sorted by
Tagged with
1 vote
0 answers
54 views

Problem fitting LMM to swaptions

I don't know what I am doing wrong. My goal is to calibrate correlations between my brownian motions. For that I simulate forwards paths and then calculate Swaptions rates. I use Euler Method to ...
1 vote
2 answers
1k views

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\...
2 votes
2 answers
522 views

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 ...
2 votes
3 answers
3k views

TED Spread Replacement?

Will replacing the 3-month tenor of the US LIBOR with SOFR or CME 3-Month SOFR Futures work as well as an indicator of credit risk? I have my doubts given: SOFR reflects secured lending LIBOR is ...
2 votes
2 answers
5k views

Libor OIS basis swap equation

I'm a little embarrassed about this because I have a PhD in math, but I'm having a little trouble working out how to bootstrap an OIS curve from libor rates and basis swap rates. If I had an equation ...
4 votes
1 answer
843 views

Accrued interest calculation for floaters linked to O/N rates (such as SOFR)

It is known that between 2021 and 2022, LIBOR rates will cease to exist. Therefore bond issuers started to link their newly issued floaters to O/N rates based on actual trades such as SOFR for USD or €...
1 vote
0 answers
43 views

EURIBOR dependent product pricing

3M Euribor rates still exists (see https://www.ice.com/) and there still exist structured products depending on them : for instance a CMS spread whose udnerlying CMS rates depend on it. But also range ...
0 votes
0 answers
75 views

Do RFR swaps fix in advance or arrears?

Consider the floating leg of a IRS on the RFR which is effective today at $t_1$ and has a payment at $t_1 + 3M$. My question is, when the payment occurs at $t_1 + 3M$, is this the $3M$ forward rate ...
0 votes
0 answers
52 views

Explicit pythonic building of Flat Forward Curve using Changes assumed from central bank meetings to price FRAs

This question is related to the following questions asked previously, primarily the first: Using QuantLib to build Flat Forward Curve using Changes assumed from central bank meetings to price FRAs ...
1 vote
1 answer
149 views

Using QuantLib to build Flat Forward Curve using Changes assumed from central bank meetings to price FRAs

What I am trying to do is price EURIBOR6M FRAs using a curve built in quantlib with changes in rate due to central bank meetings. For concreteness, my goal is to price EURIBOR6M FRAs, say 1x7 FRA, ...
0 votes
1 answer
62 views

How do we determine 0M spot rate for 3M libor?

Say I have a 3M libor curve constructed from a bunch of 3M FRAs, so I have a 3M spot rate, a 6M spot rate, a 9M spot rate, etc. For points in-between, say 4M, I would have to interpolate between the ...
0 votes
0 answers
185 views

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 ...
2 votes
0 answers
157 views

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 ...
0 votes
2 answers
490 views

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 ...
2 votes
1 answer
174 views

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 (...
1 vote
0 answers
179 views

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 ...
2 votes
1 answer
318 views

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)?
1 vote
1 answer
91 views

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 ...
0 votes
1 answer
225 views

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 ...
4 votes
1 answer
2k views

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 ...
5 votes
1 answer
5k views

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). ...
0 votes
1 answer
245 views

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/...
0 votes
1 answer
207 views

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 ...
1 vote
4 answers
1k views

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 ...
2 votes
1 answer
318 views

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 (...
7 votes
1 answer
270 views

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) +...
2 votes
0 answers
98 views

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 ...
16 votes
3 answers
3k views

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 ...
2 votes
1 answer
720 views

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 ...
0 votes
1 answer
85 views

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 ...
5 votes
1 answer
290 views

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 ...
2 votes
0 answers
100 views

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}...
3 votes
1 answer
216 views

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)...
2 votes
1 answer
291 views

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}}{\...
2 votes
1 answer
364 views

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^...
2 votes
0 answers
960 views

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 ...
5 votes
3 answers
15k views

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 ...
0 votes
1 answer
291 views

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 ...
3 votes
2 answers
564 views

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 ...
9 votes
1 answer
605 views

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 ...
0 votes
0 answers
92 views

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 ...
1 vote
1 answer
10k views

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 ...
0 votes
0 answers
62 views

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 ...
0 votes
0 answers
224 views

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 ...
3 votes
1 answer
1k views

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 \...
1 vote
2 answers
5k views

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 ...
6 votes
1 answer
574 views

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 ...
1 vote
1 answer
447 views

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 ...
8 votes
2 answers
1k views

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 ...
1 vote
1 answer
66 views

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 ...