170 Frequently Asked Questions In Quantitative Finance
How Do I Dynamically Hedge?
Short Answer
Dynamic hedging, or delta hedging, means the continu-
ous buying or selling of the underlying asset according
to some formula or algorithm so that risk is eliminated
from an option position. The key point in this is what
formula do you use, and, given that in practice you
can’t hedge continuously, how should you hedge dis-
cretely? First get your delta correct, and this means
use the correct formula and estimates for parameters,
such as volatility. Second decide when to hedge based
on the conflicting desires of wanting to hedge as often
as possible to reduce risk, but as little as possible to
reduce any costs associated with hedging.
Example
The implied volatility of a call option is 20% but you
think that is cheap, volatility is nearer 40%. Do you put
20% or 40% into the delta calculation? The stock then
moves, should you rebalance, incurring some inevitable
transactions costs, or wait a bit longer while taking the
risks of being unhedged?
Long Answer
There are three issues, at least, here. First, what is the
correct delta? Second, if I don’t hedge very often how
big is my risk? Third, when I do rehedge how big are
my transaction costs?
What is the correct delta? Let’s continue with the above
example, implied volatility 20% but you believe volatility
will be 40%. Does 0.2 or 0.4 go into the Black–Scholes
delta calculation, or perhaps something else? First
let me reassure you that you won’t theoretically lose
