Questions tagged [libor-market-model]

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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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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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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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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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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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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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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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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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Where to find Caps/Floor historical data?

I'm trying to calibrate the Lognormal Forward Libor Model to market data, in order to calculate market implied volatilities. However, I'm having some troubles finding any Cap/Floor historic price. Not ...
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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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