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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 ...
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 theorem is especially important in the theory of financial mathematics as it explains how to convert from the physical measure, which describes the probability that an underlying instrument (such as a share price or interest rate) will take a particular value or values, to the risk-neutral measure which is a very useful tool for evaluating ...
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 .
For (ii) on value at risk, or "VaR", an estimate of how much the investment or area in question might lose with a given probability in a set time period, with the bank holding "economic"-or “risk capital” correspondingly; common parameters are 99% and 95% worst-case losses - i.e. 1% and 5% - and one day and two week horizons. [28]
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 .
Importance sampling consists of simulating the Monte Carlo paths using a different probability distribution (also known as a change of measure) that will give more likelihood for the simulated underlier to be located in the area where the derivative's payoff has the most convexity (for example, close to the strike in the case of a simple option ...
Short-rate tree calibration under BDT: Step 0. Set the risk-neutral probability of an up move, p, to 50% Step 1. For each input spot rate, iteratively: . adjust the rate at the top-most node at the current time-step, i;