The Delta Of An Option, Part II
Suppose a stock is selling for $50 and the value of the 50 call with a few
months left before expiration is $4. How much will the value of the call
increase if the underlying price moves to $52?
You can use delta to estimate the value of the option at the new stock price. An at-the-money option typically has a delta of about 0.5, so suppose it
is exactly 0.5. The value of the call will increase by about 0.5 times the
increase in the stock price, or 0.5 times $2 = $1. So the value of the option
will be about $5 if the stock moves up $2.
The price of the option is a different story. Although the value is $4,
the
option may well be underpriced and selling for, say, $3. When the option’s
value moves to $5, it is unlikely the option price will remain at $3
(although of course it could). When the stock is at $50 and the option value
is $4, a call option price of $3 represents a price-to-value ratio of 0.75. If the
stock moved to $52 and the call price remained $3, the price-to-value ratio
would decline to 0.6, low enough to attract some attention and presumably some
buyers.
This illustrates the delta of an option does not tell you how the
option price will move in relation to the underlying’s movement, but rather
how the option’s value will change. Price often follows value, and by looking more
underpriced than before and attracting buyers, the call’s price will
probably move up in the above case.
Also, the method of using delta to estimate the change in option value
works only for small changes in the price of the underlying. If the underlying
moved to $60, a $10 increase, the call value at the new price is not well
estimated by this calculation. You can see this clearly here, as this method
would give an estimated value of $4 + (0.5*$10) = $4 +$5 = $9, less even than the
intrinsic value of the call, $10, when the underlying is at $60.
Likewise, if the stock price fell to $42, we know the option still
would have some value even though it would be currently out-of-the-money. But
the estimation using delta would give it a value of $4 – (0.5*$8) = $4 – $4 = 0.
The delta of an option is useful for estimating changes in the option’s
value for small changes in the price of the underlying, but is only useful for
getting a ballpark estimate of the option’s price for small changes in the
price of the underlying, and should not be used for estimating either price or value
for larger changes in the price of the underlying.