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For example, for bond options [3] the underlying is a bond, but the source of uncertainty is the annualized interest rate (i.e. the short rate). Here, for each randomly generated yield curve we observe a different resultant bond price on the option's exercise date; this bond price is then the input for the determination of the option's payoff.
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
The 5% Value at Risk of a hypothetical profit-and-loss probability density function. Value at risk (VaR) is a measure of the risk of loss of investment/capital.It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day.
Under the assumption of normality of returns, an active risk of x per cent would mean that approximately 2/3 of the portfolio's active returns (one standard deviation from the mean) can be expected to fall between +x and -x per cent of the mean excess return and about 95% of the portfolio's active returns (two standard deviations from the mean) can be expected to fall between +2x and -2x per ...
Every output random variable from the simulation is associated with a variance which limits the precision of the simulation results. In order to make a simulation statistically efficient, i.e., to obtain a greater precision and smaller confidence intervals for the output random variable of interest, variance reduction techniques can be used ...
Algorithmic trading is a method of executing orders using automated pre-programmed trading instructions accounting for variables such as time, price, and volume. [1] This type of trading attempts to leverage the speed and computational resources of computers relative to human traders.
A main assumption in linear regression is constant variance or (homoscedasticity), meaning that different response variables have the same variance in their errors, at every predictor level. This assumption works well when the response variable and the predictor variable are jointly normal. As we will see later, the variance function in the ...
The canonical tail value at risk is the left-tail (large negative values) in some disciplines and the right-tail (large positive values) in other, such as actuarial science. This is usually due to the differing conventions of treating losses as large negative or positive values.