DIGITAL OPTIONS THE MOLECYLS OF OPTION PRICING
The figure to the left
illustrates the payoff from a very simple option. The option pays
a cash amount at maturity equal to K if asset one S1 at maturity
is between level X1 and X2, and asset two S2 simultaneously is between
X3 and X4. This is a simple type of two-asset digital option.
If you know how to price one of this you can just combine a lot
of these together to engineer almost any option payoff profile you
want. The formulas for this and several other digital/binary options
can be found in: The Complete Guide to Option
Pricing Formulas.
Most published formulas for digital/binary options assume geometric
Brownian motion. But you could easily extend this approach to also
working when assuming stochastic volatility, mean reverting, seasonallity
or whatever process you prefer. It could be that you then not can
find a closed form solution. In that case I would recommend you
to take a close look at Quasi-Monte
Carlo simulation.
Once again the only limit
will be your fantasy. If you have a fantasy similar to mine that
means no limits! |