Hi Mark,

'This is sometimes called the pathwise method. The main difficulty

with this method is how to interpret f'(ST) when f is discontinuous. Jump discontinuities

will give rise to delta functions in the derivative. We can therefore write

f = g + h, with g continuous and h piecewise constant. Then g' is well-behaved,

and its contribution to the Delta can now be evaluated by Monte Carlo. The derivative

of h is a sum of Delta functions so the integral can be computed analytically

as a finite sum and we are done.'

Can you explain how the last sentence can be applied to a simple example of a digital call? (though such simple product is not evaluated through MC in practice). I know we can use smoothing technique to approximate the digital payoff using cumulative normal distribution. Appreciated if you could tell me there is a way to compute it analytically.

Many thanks.

regards,

Kelvin