# Instantaneous Volatility and Correlation in the LIBOR Market Model

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## Description

This experiment shows that it is possible to change the terminal correlation of LIBOR rates even if these rates are driven by the same one dimensional brownian motion (i.e. having instantaneous correlation of 1). A change in the terminal correlation of LIBOR rates will change the price of swaptions, but of course not the price of caplets.

It serves as a companion to Chapter 21 of Mathematical Finance.

### Predefined Scenarios

Your may step through five predefined scenarios.

Scenario 1 |
Scenario 2 |
Scenario 3 |
Scenario 4 |
Scenario 5 |

A one factor model. |
A three factor model. |
A five factor model. |
A one factor model leading to terminal decorrelation through different volatility structures. |
A one factor model with similar caplet prices and terminal correlation as Scenario 1, but different terminal variance of L(5.5,6.0) at t=5.0 and thus different swaption prices (compared to Scenario 1). |

The scenarios 1-3 show the influence of the instanteneous (de-)correlation on the terminal correlation. The scenarios 4 and 5 show the influence of a time (and LIBOR) dependent volatility structure on the terminal corrlation

© Copyright 2007,2013 Christian P. Fries