First-order Greeks: Five letters to read an option

An option's price depends on several things at once. To find their way, professionals use Greek letters.

Each letter answers a single question: if this thing moves a little, how much does the option's price move?

Take an example. A share is worth one hundred euros. A call option at one hundred euros, in three months, costs say five euros.

It gives the right to buy the share at one hundred euros. The more the share rises, the more this right is worth.

First letter: delta. How much does the option move when the share moves one euro?

Say a delta of zero point five. The share gains one euro, the option gains about fifty cents.

If the share rises well above one hundred euros, delta approaches one. If it falls well below, it approaches zero.

Second letter: vega. It is not a real Greek letter, but everyone uses it.

Vega measures sensitivity to implied volatility: the agitation the market expects from here on.

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Say a vega of twenty cents. If expected agitation gains one point, the option gains twenty cents, even if the share does not move.

Third letter: theta. It is what time costs, each day, the person holding the option.

Say three cents a day. Nothing moves, and yet the option loses value. Each passing day wears the right down.

And the wear speeds up as expiry approaches. For an option like this one, the last month costs more than the first.

Fourth letter: rho. Sensitivity to interest rates.

Why rates? Buying the option rather than the share leaves money invested meanwhile. The higher rates are, the more this right is worth.

Say twelve cents per point of rate. Over three months, it is often the letter people look at least.

Fifth letter: lambda. It is delta, but in percentage terms. It is also called elasticity.

The share gains one per cent, so one euro. The option gains fifty cents on five euros: ten per cent.

A lambda of ten. In percentage terms, the option moves ten times faster than the share. In both directions.

That is the leverage hidden in an option. And like all leverage, it multiplies losses too.

To sum up. Delta: the share. Vega: expected agitation. Theta: time. Rho: rates. Lambda: delta in percentage.

These letters themselves change at every moment. Today's delta is not tomorrow's.

They are approximations, accurate for small moves. A big shock goes beyond them.

But they turn an opaque price into a few simple answers. That is why trading floors speak Greek.