It is common in finance for the core essence of an idea to be hidden behind
complex language and the liberal use of mathematics. One of the objectives of
the derivatives section of the Financial Pipeline is to make the revolution in
financial engineering accessible to everyone so that people can make informed
decisions about the opportunities derivative instruments present and the
pitfalls they create.
In previous articles we have compared products with linear
payoff profiles to instruments with non-linear payoff profiles and we learned
that only non-linear products have time value. We talked about the true meaning
of time value to a derivatives professional and the question he must ask
himself when evaluating a particular structure.
"If I buy this structure, will I be able to make more
money trading the underlying cash instrument than I will pay in time decay over
the life of the instrument?" (Conversely, he could have asked himself, "If I sell this product, will the losses I sustain trading the
underlying cash instrument against this structure be less than the premium I am
paid at inception?").
Let us restrict ourselves to the question facing the
prospective buyer of this non-linear instrument. Think of it as a call option
on a particular stock, say Dollar.com. For the purpose of argument, assume that
the current stock price is $100, our option's notional amount is 100 shares,
the options matures in 3 months and the strike price is $100.
In evaluating this central question of value, there are two
important factors that stand out: volatility and time. We will consider them
one at a time.
The higher the implied volatility of this product, the higher the premium will be and the more difficult it will
be to pay for the option. However, if we expect actual volatility to be higher
than the implied volatility, it may pay for us to own this option and to trade
GE stock against it.
The key here is our expectation of what volatility will
actually turn out to be as it relates to the implied volatility.
For example, if implied volatility on our Dollar.com call is
15% (on an annualized basis) in the marketplace but we think that actual
volatility will be closer to 25%, we should buy the option. We will make more
money delta-hedging the option (or rebalancing the delta in response to market
movements) than we will pay in premium. See previous articles for an
explanation of delta-hedging.
Now, what does it mean if implied volatility for our option in the
marketplace jumped from 15% to 25% immediately after we bought our option. This
might happen if there was an unexpected announcement from a takeover company,
Savage LBO LLC, that they were going to make an unfriendly bid for Dollar.com.
The outcome is uncertain.
First, we will see the premium jump higher for the option we
own. We will own something that has increased substantially in value. Because
the option is at-the-money spot (i.e. its strike is equal to the current spot
rate), this effect is at a maximum. Recall that the change in the option's
value due to a change in implied volatility, all other things being equal, is
its vega.
Second, we can see that the 3 month call we bought at an
implied volatility of 15% is now worth what a 6 month call with the same strike
before volatilities shot up in response to the announcement. Therefore, the
move higher in implied volatilities is like an extension of our 3 month option
into a 6 month option. It is as if we got 3 months for free.
Time value is the measure of how
much money we should make if the stock turns out to be as volatile as the
implied volatility says it should be. Changes in implied volatility necessarily
mean changes in time value (and therefore premiums). We could make the same
absolute amount of money delta hedging a short-dated option on a very volatile
underlying as we could on a long-dated option on a calm underlying.
Article by Chand Sooran, Principal Victory
Risk Management Consulting, Inc. |