### The Call Option Valuation Wedge (movable)
The following picture is the the wedge-shaped solid, the volume of which is
used as the basis for the valuation of the call option according to the method
of Black-Scholes and Merton. You can rotate this with the mouse, and zoom by
holding shift.
Notice that this displays two wedges, one corresponding to a safer stock,
with a taller, more peaked probability distribution (and thinner tails) and one
corresponding to a riskier stock, that has a flatter distribution of prices and
fatter tails.
The point of the graph is to illustrate that calls on riskier stocks are more
valuable. This is a counterintuitive notion in abstract, particularly since
riskier goods are less desirable, hence less valuable. Seeing the
call-valuation wedge should indicate why the call on the riskier stock is more
valuable: Its fatter tail adds a lot to its volume compared to the volume that
is added because of the thinner tail of the safe stock because of the large
option payouts that correspond to this region. The higher peak of the safe stock
stock does not compensate for the lost volume because this exists in the thin
part of the wedge, where the option payouts are small.
If you are perplexed because the two distributions appear to not be located
at the same mean, you are very observant! The peaks of the two distributions do
not coincide, although their means are the same, because the distribution used
is the LogNormal, which is not symmetric. Since only one tail exists to become
fatter as standard deviation increases, the peak moves away from the tail to
maintain the mean constant.
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