Questions tagged [lmm]

The LIBOR market model is a financial model of interest rates. It is used for pricing interest rate derivatives. The quantities that are modeled are a set of forward rates (also called forward LIBORs), which have the advantage of being directly observable in the market, and whose volatilities are naturally linked to traded contracts.

Filter by
Sorted by
Tagged with
1 vote
1 answer
74 views

Pricing & hedging vanilla interest rate options with SABR LMM

Are there any advantages of pricing and hedging plain vanilla interest rate options with more complex SABR LMM instead of simpler SABR model? Should one always go with the SABR LMM as a universal ...
user avatar
  • 535
1 vote
1 answer
75 views

SABR LMM vs no-arbitrage term structure of SABR parameters

There exists a LIBOR Market Model with stochastic volatility for pricing and hedging exotic (e.g. path-dependent) interest rate options with smile. However let us consider the following approach: ...
user avatar
  • 535
7 votes
1 answer
165 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) +...
user avatar
  • 428
3 votes
0 answers
96 views

SABR LMM for RFR

Is there a research showing a way to use SABR LMM with new RFRs such as SOFR, i.e. pricing exotic path-dependent RFR derivatives with volatility smile and skew? I'm aware that Looking Forward to ...
user avatar
  • 535
0 votes
1 answer
46 views

Reconciling different specifications of drifts in the LMM

I've been going through the book "Fixed Income Securities" by Bruce Tuckman which gives the following definitions of the drift terms (after showing it for a specific example with 3 forward ...
user avatar
  • 788
6 votes
0 answers
149 views

SABR-LMM: best way to perform a MC simulation

I am working on a SABR-LMM model with the following system of SDEs under a numeraire $N$: $$ \begin{align} &\mathrm{d} F_i(t) = \sigma_i (t) (F_i(t) + s)^{\beta} \Big( \mu^f_i (t) \mathrm{d}t ...
user avatar
  • 428
0 votes
1 answer
59 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 ...
user avatar
2 votes
1 answer
408 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 ...
user avatar
  • 5,211
1 vote
1 answer
194 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 (...
user avatar
  • 5,211
7 votes
1 answer
198 views

Benchmark a Libor Market Model implementation

Assume I have implemented a solution of the Libor Market model PDE in terms of the Finite Difference method. What is a good strategy for validating and benchmarking the results of this implementation? ...
user avatar
  • 308
3 votes
0 answers
133 views

Change of measure for BGM (LMM) Model

I've been checking the demos for BGM (LFM) forward rate model. Here's a short reminder to help you follow: Now, take the following $$\frac{dL_j(t)}{L_j(t)} = \sigma_j. dW^j(t) = \mu_{ij} dt + \...
user avatar
  • 210
1 vote
2 answers
126 views

LIBOR Market Model - tenors?

In the LIBOR market model, we have a bunch of forward rates $L_j$ on $[T_j, T_{j+1}]$ for some collection on $j$. My question is, is it the delivery dates or the time to maturities that are fixed? So ...
user avatar
0 votes
1 answer
181 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/...
user avatar
0 votes
1 answer
343 views

Calibrate SABR-LMM using only data from Bloomberg?

I'm exploring the SABR-LMM model. In particular, have been trying to study the effect of the parameters and their time evolution. However, the data seems to be a major issue here. Prices for caps/...
user avatar
3 votes
1 answer
447 views

Libor Market Model (LMM) under risk neutral measure

I would like to establish the equations of forward libors under risk neutral measure. Here is how I do it, and what I get : Under the $P_{T_j} $ measure, forward Libor $L_j$ is martingale. Thus: $$ ...
user avatar
1 vote
0 answers
495 views

The "I want to price swaptions" request

In a small buy-side structure I recently had the following request : "I want to trade swaptions, I need to price them". After a quick discussion the need is to price vanilla options on fix vs float ...
user avatar
  • 1,162
0 votes
2 answers
1k views

Accreting swaption

Is there any literature on the maths behind the computation of the price of an accreting swaption in the LMM model (no monte carlo, closed formula or close enough...)? Thank you!!
user avatar
  • 177
4 votes
0 answers
147 views

Volatility Parametrization Libor Market Model - Underspecified Model?

Does the volatility parametrization that I have chosen give an underspecified model? Which volatility parametrization in the Libor Market Model would suit the best for the particular case described ...
user avatar
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 ...
user avatar
0 votes
1 answer
108 views

Prove Volatility Parametrization of Libor Market Model is Bounded/Not Bounded

How can I prove that the function $$\sigma_i\left(t\right) = k_i\left[\left(a+b\left(T_i-t\right)\right)e^{-c\left(T_i-t\right)}+d\right]$$ is bounded/unbounded? $\sigma_i\left(t\right)$ is the ...
user avatar
1 vote
0 answers
575 views

Pricing back swaptions corresponding to underlying swaps of Bermudan Swaption in calibrated LMM

I do not know to which swaption volatility matrix I have to calibrate the LMM in order to price back correctly the swaptions corresponding to the underlying swaps of a Bermudan Swaption. My problem: ...
user avatar
2 votes
1 answer
267 views

Numerical Optimizer Matlab Calibration LMM

I am trying to mimimize the following function in order to calibrate the Libor Market Model $$\sum_{i=1}^{n} \left(\sigma_i^{market}-\sigma_i^{Reb}\left(a,b,c,d,\beta\right)/\sqrt{T_i}\right)^2,$$ ...
user avatar
2 votes
1 answer
1k views

instantaneous forward rates vs forward LIBOR rates

HJM describes the behavior of instantaneous forward rates while BGM describes the behavior of forward Libor rates. From concept perspective, I understand forward libor rate are like forward Libor rate ...
user avatar
-1 votes
1 answer
302 views

Finding Discount Bond Matrix in LMM Model C++

I am working on a 1 Factor Libor Market Model (LMM) in C++ and I working my implementation of the formula to find my Discount Bond matrix via the following formula: In the case of my model alpha is ...
user avatar
  • 139
0 votes
1 answer
160 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 ...
user avatar
7 votes
2 answers
1k views

Practical implementation of Libor Market Model

I am trying to implement a project about the BGM model, suggested in the book "The Concepts and Practice of mathematical finance" by Mark Joshi. My question is related to the forward volatility ...
user avatar
  • 463
1 vote
0 answers
110 views

Price 3m libor autocap with LMM calibrated on 1y swaption data

I need to calculate a price of an autocap contract which is An autocap is similar to a cap, but at most γ ≤ β caplets can be exercised, and they have to be automatically exercised when in the ...
user avatar
  • 156
2 votes
1 answer
564 views

LMM. Calibration to swaptions by Brigo and Morini. Volatility of swaption that matures at T=0

I'm reading Brigo D., Mercurio F. Interest Rate Models - Theory and Practice (Springer, 2006)(ISBN 3540221492) and also a source article on LMM cascade calibration to swaptions by Brigo and Morini. I ...
user avatar
  • 156
1 vote
0 answers
327 views

Incompatibility of Lognormal Forward Model (LMM\BGM) and Lognormal Swap Model

In his paper On the distributional distance between the Libor and the Swap market models (and also in his book about IR modeling) D.Brigo says: 10, 11, 12 are defined in the end of message. Do I ...
user avatar
  • 156
0 votes
0 answers
843 views

Calibration Problem in the LMM-Skew (Shifted Diffusion) Model

I have implemented the LIBOR market model (LMM) and I am quite satisfied with the results. I have now added a skew to the model as described in 10.1 of Brigo/Mercurio. That is, I have replaced the SDE ...
user avatar
4 votes
2 answers
502 views

question on Leif Andersen's "Interest Rate Modeling, vol 2 Term Structure Models"

I'm reading Leif Andersen's "Interest Rate Modeling, vol 2 Term Structure Models" and met a problem on Chapter 14 LM Dynamics and Measures, $\S$ 14.2.5 Stochastic Volatility, Lemma 14.2.6, on page 602....
user avatar
  • 2,107
14 votes
2 answers
1k views

When is the LIBOR market model Markovian?

The question is inspired by a short passage on the LMM in Mark Joshi's book. The LMM cannot be truly Markovian in the underlying Brownian motions due to the presence of state-dependent drifts. ...
user avatar
  • 4,910
15 votes
3 answers
2k 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 ...
user avatar
  • 3,212