A question on Monte Carlo Simulation

[Patrick Pan]

Hi David,

In Jorion's VaR, Ch12, P315 (Also in video slides)

"The current value of derivatives is obtained from discounting at risk-free rate and averaging across all experiments, that is
f(t)=E*[e^-rtF(St)]"

The order for this calculation is: discount each future value back to current time, then average among the current values.

Is the other order of calcalation a valid option?
f(t)=e^-rtE*[F(st)]

In other words, is it ok to calculate the average across all future value and only discount the expected future value back to current?

If it really make sense, is this method more effcient because it save the most of discounting?

Thanks

Patrick

 

[David Harper CFA FRM]

Hi Patrick - if (t) is constant for all simulations, then e^(-rt) is a constant (a = e^(-rt), then by distributive property, I am forced to agree with you: (sum of [a*F(St)])/n = a*(sum of [F(St)])/n

...my first instinct was that Jorion's is more robust because it allows for various maturities; e.g, if American options, then exercises not all at time (t) and yours won't handle various time to exercise. But I see he doesn't claim it to apply to Americans, so frankly I do not know why it is expressed this way (my only guess is that it consistent with more robust and he didn't bother to further simplify; I certainly can't see any distributional assumption violation). David