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The probability of default is an estimate of the likelihood that the default event will occur. It applies to a particular assessment horizon, usually one year. Credit scores, such as FICO for consumers or bond ratings from S&P, Fitch or Moodys for corporations or governments, typically imply a certain probability of default.
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 .
In subsequent research, Merton's model has been modified to capture a wider array of financial activity using credit default swap data. For example, Moody's uses it in the KMV model both to calculate the probability of credit default and as part of their credit risk management system. The Distance to Default (DD) is another market-based measure ...
This notion is captured in the so-called "hedging irrelevance proposition": [16] "In a perfect market, the firm cannot create value by hedging a risk when the price of bearing that risk within the firm is the same as the price of bearing it outside of the firm." In practice, however, financial markets are not likely to be perfect markets.
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.
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.
The Jarrow–Turnbull model is a widely used "reduced-form" credit risk model. It was published in 1995 by Robert A. Jarrow and Stuart Turnbull. [1] Under the model, which returns the corporate's probability of default, bankruptcy is modeled as a statistical process.