272 Frequently Asked Questions In Quantitative Finance
Today
Figure 4-3:The curve is approximately quadratic.
To calculate how much interest we received we need to
know how much money we put in the bank. This was
×S
from the stock sale and
−V
from the option purchase. Therefore the interest we
receive is
r(S−V)δt.
Finally, look at the money made from the stock move.
Since gamma is positive, any stock price move is good
for us. The larger the move the better.
The curve in Figure 4-3 is locally quadratic, a parabola
with coefficient^12 . The stock move over a time period
δtis proportional to three things:
- the volatilityσ
- the stock priceS
- the square root of the time step
Multiply these three together, square the result because
the curve is parabolic and multiply that by^12 and you
