The shortcut premium

Say a trader wishes to price an At-the-Money option (which is somewhat close to expiry) and is not in front of his tablet or a computer. Well, the lazy mind has its ways of approximations.

A quick and dirty way to price such an option (use this only if you are in a pub with a pint and do not want to be overly fleeced by the seller) is as follows:

Price=0.4*Volatility*Squareroot(Time)*Underlier Value

Very Straightforward indeed. A simple example would suffice.

Take time to expiry (in years) as 0.1; Let volatility be a range from 0.05 to 0.7 (that is from 5% to 70%) with an increment of 0.05 and let 100 be both the Strike and the price of the underlying.

Both the prices (across vols) are given in the table for the reader to compare.

As can be observed the approximations work pretty much in-line with theory.

Interestingly, say there is a stock paying no dividend and trading at $100. Let the riskless rate be 5% and the volatility be zero. If there be an European call struck at-the-money expiring in a year on this stock, what might it be worth? Something to ponder over and to harp on the point that life is not always about short-cuts.

Originally published at https://www.linkedin.com.