# Tag Info

### Exploding Libor Rates in Libor Market Model

this is a well-known problem. One solution is to make volatility zero when rates exceed a certain high level. It's less problematic than it looks because any cash-flows generated will be divided by ...
• 6,973
Accepted

### Forward starting zero-coupon bonds

$Z(t_0,t_1,t_2)$ is the $t_1$-forward price of the ZC bond with maturity $t_2$, as of $t_0$. We have: $$Z(t_0,t_1,t_2) = E_{t_0}^{t_1}[Z(t_1,t_2)]\not= Z(t_1,t_2).$$ With a not-trivially stochastic ...
• 5,043
Accepted

### Intuition of drift in Libor market model

Paying F(K-1) at a lag (K) is a delayed payment and involves a convexity adjustment that can be understood as a consequence of 2 parts - a "stochastic part" where if rates rise whenever F(K-...
• 2,431

### Using converted lognormal volatilities for negative rates in a lognormal Libor Market Model (LMM)

I've not seen the abs function on the forward rate here before, the approximation comes from matching variances of a Black (Lognormal) and Bachelier (Normal) SDE. The Black SDE doesn't have this ...

### Accreting swaption

From a practitioner standpoint, we know the prices of non accreting swaptions. The price of the accreting swaption in any model calibrated to these non accreting swaptions, is heavily dependent on ...
• 17.2k
Accepted

### Pricing Swaption Analytically using Libor Market Model

The present value of a Vanilla Swap (the word Vanilla is used since I am considering the simplest swap, i.e., notional equal to one, contiguous time intervals, constant rate, etc) is given by: \begin{...
• 741
Accepted

• 741

### LIBOR Market Model - tenors?

Just to be precisely clear, your mathematical formulation will not necessarily capture the nuances of the physical dates that libor is valued between, due to holiday calendars and modification rules. ...
• 10.7k
Accepted

### SABR LMM vs no-arbitrage term structure of SABR parameters

I am guessing that the first model you are referring to is the one from Rebonato: Linking caplets and swaptions prices in the LMM-SABR model (2009)? If yes, then I would say that your approach is a ...
• 428
The cash bond doesn't require a displacement, as such the denominator in your drift term should be $F_k(t)$ not $\bar{F}_k(t)$, i.e. \$dF_k(t) = \sigma_k(t)\bar{F}_k(t)\sum^k_{j=\beta(t)}\frac{\tau_j\...