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CDS provide risk-neutral probabilities of default, which may overestimate the real world probability of default unless risk premiums are somehow taken into account. One option is to use CDS implied PD's in conjunction with EDF (Expected Default Frequency) credit measures.
The absence of arbitrage is crucial for the existence of a risk-neutral measure. In fact, by the fundamental theorem of asset pricing, the condition of no-arbitrage is equivalent to the existence of a risk-neutral measure. Completeness of the market is also important because in an incomplete market there are a multitude of possible prices for ...
where is the maturity of the longest transaction in the portfolio, is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity , is the loss given default, is the time of default, () is the exposure at time , and (,) is the risk neutral probability of counterparty default between times and .
The Merton model, [1] developed by Robert C. Merton in 1974, is a widely used "structural" credit risk model. Analysts and investors utilize the Merton model to understand how capable a company is at meeting financial obligations, servicing its debt, and weighing the general possibility that it will go into credit default.
For credit risk, [104] sensitivities are measured via CS01, while analysts use models such as Jarrow–Turnbull and KMV to estimate the (risk neutral [105]) probability of default, hedging where appropriate, usually via credit default swaps.
The First-to-Default probability, or the probability of observing one default among a number of institutions, has been proposed as a measure of systemic risk for a group of large financial institutions. This measure looks at risk-neutral default probabilities from credit default swap spreads.
As regards the construction, for an R-IBT the first step is to recover the "Implied Ending Risk-Neutral Probabilities" of spot prices. Then by the assumption that all paths which lead to the same ending node have the same risk-neutral probability, a "path probability" is attached to each ending node.
The equivalent martingale probability measure is also called the risk-neutral probability measure. Note that both of these are probabilities in a measure theoretic sense, and neither of these is the true probability of expiring in-the-money under the real probability measure.