Encyclopedia of Quantitative Finance, IV Volume Set

Jamshidian Formula see Bond Options

Jamshidian Model see Swap Market Models

Jarrow–Lando–Turnbull Model

The credit-risk model of Jarrow, Lando, and Turnbull is based on a Markov chain with finite state space, modeled in discrete or continuous time. Economically, it relies on the appealing interpretation of using different rating classes, which are represented by the states of the Markov chain. Presumably, it is the first credit-risk model that incorporates rating information into the valuation of defaultable bonds and credit derivatives. An advantage of modeling the credit-rating process is that the resulting bond prices explicitly depend on the issuer’s initial rating and possible rating transitions in the future. Moreover, the model allows to price derivatives whose payoffs depend on the credit rating of some reference bond, an application that is not straightforward in intensity based models or structural-default models.

Technically, the model is formulated on a filtered probability space with a money-market account B = {B(t)}_0≤t≤T as numéraire. The state space of the underlying Markov chain is denoted by S = {1, …, K}, where state K represents default. The other states are identified with rating classes that are ordered according to increasing default risk, that is, state 1 represents the best rating. Transition probabilities from one state to another are specified via a probability ...