Terminal Distribution
- Thread starter kkapoor
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Hi @kkapoor Terminal distribution refers to the distribution at the end of a selected, longer time horizon. For example, say an asset's daily returns are normally distributed with (return) volatility of 1.0%; this is a given assumption about the distribution over one day.
We might then ask: what is the "terminal distribution" at the end of one month? at the end of one year? If the returns are i.i.d. (which includes no mean reversion), then the "terminal distribution" at the end of one year is a normal distribution with standard deviation of 1.0%*sqrt(250) = 15.8%. We often do this without thinking too much about the implicit assumption: the one-day return is characterized by a normal distribution with stddev = 1%, and by way of assumption, we estimate that the one-year return is also normal (by way of a summation stability property) and with stddev = 15.8%. It is relevant in Tuckman's interest rate models because the models themselves generally refer to (very) short term interest rate dynamics, yet we may be interested in the "terminal distribution," including the future mean and standard deviation, at the end of a week or month or longer. Thanks,
We might then ask: what is the "terminal distribution" at the end of one month? at the end of one year? If the returns are i.i.d. (which includes no mean reversion), then the "terminal distribution" at the end of one year is a normal distribution with standard deviation of 1.0%*sqrt(250) = 15.8%. We often do this without thinking too much about the implicit assumption: the one-day return is characterized by a normal distribution with stddev = 1%, and by way of assumption, we estimate that the one-year return is also normal (by way of a summation stability property) and with stddev = 15.8%. It is relevant in Tuckman's interest rate models because the models themselves generally refer to (very) short term interest rate dynamics, yet we may be interested in the "terminal distribution," including the future mean and standard deviation, at the end of a week or month or longer. Thanks,
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