The approximation of Eq. (13.31) is sometimes suggested as a possible way to approximate V@R of option portfolios. For instance, with the data of Example 13.10, we may apply the following first-order approximation:

where we link the change in the portfolio value, \(V\), with the random return on the stock share, \(r=S S_{0}\). Say that we need the \(99 \%\) daily \(\mathrm{V} @ \mathrm{R}\). If we assume that the stock return is normally distributed, we find

where \(\quad d\) is the daily volatility of the stock share price. This may be estimated by scaling the annual volatility as follows:

where we use the square-root rule introduced in Example 2.1. The square-root rule is also the reason why we do not consider the stock share daily drift. Note that, to scale annual volatility down to daily volatility, we use 252 , which is roughly the number of trading days in one year. Hence,

Data From Example 13.10

Data From Equation  (13.31) 

Data From  Example 2.1

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SVA SSA. So r,