Dynamic Hedging Strategies
Adynamic hedging strategy typically involves two
positions:
ê A static position in a security or a commitment by a
firm. For example:
– A financial institution has written a call on a stock or
a portfolio; this call expires some time in the future
and is held by a counterparty which has the choice
of either exercising it or not.
– A U.S. firm has committed itself to sell 1000 widgets
at some defined time in the future; the receipts will
be in German marks.
ê An offsetting position in a financial contract. Typically,
this counter-balancing position is adjusted when market
conditions change; hence the name dynamic hedging
strategy:
To hedge its written call, the issuing firm decides to buy
shares of the underlying stock or portfolio. The number
of shares purchased at time t will depend on the price
of the underlying stock at t and on the amount of time
remaining until the expiration of the call. Another way of
viewing this is that the amount of stock held against the
call position depends on the probability that the option
will be exercised.
To hedge its anticipated receipt of German marks, the
firm might enter into a forward contract. This would be
a static hedge position. On the other hand, it might buy
a put option on Deutschmarks (DM), which would give
it the right to sell DM for a given dollar price; this is
still a static hedge position, though somewhat more sophisticated.
A third possibility would be to dynamically
simulate a put on the DM position, replicating it by holding
amounts of dollars and DM (these amounts changing
with market conditions).
In this article we consider some simple dynamic hedging
strategies and show how to simulate them in Mathematica.
Our discussion will lead us naturally to the consideration
of Value-at-Risk (VaR), a measure of possible
future losses which has become increasingly popular