Average
Key Average in Simulation Report refers to the average <Q> of the sample values qᵢ, i = 1, ..., N generated through a simulation of a quantity Q, where N is the number of scenarios in that simulation.
It is defined as:
<Q> = ( q₁ + q₂ + ... + qN ) / N
For example, Q may be defined as the present value of the payoff of an American option on a single stock.
Then in the iᵗʰ scenario, the simualted share prices of the underlying stock are generated for all times until the option's expiry and the value qᵢ is then calculated based on these simulated share prices.
This process is repeated for each scenario with the final result being the generation of the values qᵢ, i = 1, ..., N.
Note, <Q> is only an estimate of the theoretical mean ͞Q of the quantity Q.
<Q> converges to ͞Q as N goes to infinity.
The standard error of this approximation is given by Avg Std Dev