Risky Debt Jump Processes And Safety Covenants

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Risky Debt Jump Processes And Safety Covenants
Scott P Mason
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With a Poisson process, the instantaneous probability of information arriving in the time interval dt is Xdt, where X is the mean number of arrivals per unit time. The instantaneous probability of no information arriving is 1-Xdt, since the probability of more than one arrival, during the interval dt, is of an order less than dt. Given that information has arrived, the impact of that information on the value of the firm is deter- mined by a drawing from a distribution, f(Y), where Y = V(t + dt)
.../V(t) and V(t + dt) - V(t) is the change in firm value due solely to the Poisson event. Successive drawings from f(Y) are independent and all drawings are indepen- dent of the timing of the drawing. These firm value dynamics can be formally written as; dV ^ = (a-Xk)dt + dq where ct is the instantaneous expected rate of return on the firm per unit time, dq is the Poisson process and k = E[Y-1], where (Y-1) is the random variable percentage change in firm value given the occurrence of a Poisson event and E is the expectations operator.

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