# 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.

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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 (...
0answers
114 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? ...
0answers
81 views

### Displaced diffusion LMM

In the standard LMM a rate $L_i(t)=L(t,T_{i-1},T_i)$ has under the $T_n$-forward measure ($n>i$) the dynamics d{L_i}(t) = - {\sigma _i}(t){L_i}(t)\sum\limits_{j = i + 1}^n {\frac{{...
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337 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 ...
4answers
974 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 ...
2answers
762 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!!
0answers
135 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 ...
1answer
100 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 ...
0answers
468 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: ...
1answer
248 views

### Numerical Optimizer Matlab Calibration LMM

I am trying to mimimize the following function in order to calibrate the Libor Market Model $$\sum_{i=1}^{n} \left(\sigma_i^{market}-\sigma_i^{Reb}\left(a,b,c,d,\beta\right)/\sqrt{T_i}\right)^2,$$ ...
1answer
804 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 ...
1answer
248 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 ...
1answer
134 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 ...
2answers
894 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 ...
1answer
500 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 ...
0answers
105 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 Ī³ ā¤ Ī² caplets can be exercised, and they have to be automatically exercised when in the ...
0answers
311 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 ...
0answers
751 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 ...
2answers
473 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....
3answers
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 ...
2answers
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. ...