Option Greeks

The Greeks describe how an option premium moves if one input moves and the others stay still. That last clause is the one traders drop. In a real session the underlying, the implied volatility, and the clock all move together. Delta is the directional exposure. A deep in-the-money call has a delta near 1 and behaves like the share. An at-the-money option is near 0.5 in the simple model. An out-of-the-money option has a small delta and a large percentage dependence on volatility and time. Gamma is how fast that directional exposure itself changes. It is highest for short-dated at-the-money options, which is why expiry week is violent for hedgers. Theta is the bleed if nothing else happens. Vega is the exposure to the market's price of future movement. Rho is usually the small one for short-dated equity options and is not small for long-dated ones.

Read delta if you want to know the directional bet in share-equivalent terms. A portfolio of short options can be delta-flat and still be dangerous, because gamma and vega remain. Read gamma if you want to know whether the directional exposure will grow as you get wrong. Short gamma means a move against you increases the exposure that is already hurting. Long gamma means a move in your favour increases the exposure that is helping, which is why long-gamma positions are bought as protection and why they cost theta. Read vega if the trade is really a volatility trade. A long call bought before earnings is often a long-vega bet that loses even if you guess the direction, if the implied volatility collapses after the event. Theta is the bill for being long gamma and long vega. There is no Greek that is free.

Use the Greeks to see which risk you actually took. If you sell a put because you want to buy the stock lower, you are short a put: short delta is not your situation, you are long delta, short gamma, short vega, and long theta. State it that way and the earnings gap stops being a surprise. If you buy a debit spread, know that you cut vega and theta as well as cost, and that the spread has a maximum value. For a book, sum the Greeks only across positions you can actually offset. A short-dated gamma and a long-dated gamma do not cancel in any practical hedging sense. Hedge the horizon you have, or do not pretend the net number is a hedge.

Treating delta as a probability. In the simple model it is related to a risk-neutral probability and it is still not the chance you personally make money after costs. Also holding "all else equal" in your head while volatility is repricing. And selling options because theta is positive, without computing the gamma loss on a one-day move of ordinary size. Positive theta that is smaller than a routine gamma loss is not income. It is an underpriced risk. Finally, mixing a Greek quoted per one point of the underlying with one quoted per one percent. Desks do this to themselves. Read the header.

Greeks are local. They describe a small move. A gap of several percent makes the delta you calculated last night a poor guide, which is why gamma exists and why it too is only a local correction. They are model-dependent. Volatility smile, dividends, early exercise, and borrowing costs all move the numbers. Published Greeks can be stale in a fast market. And a Greek is not a position. You cannot exit "vega" if the strike you need is wide or halted. Use the sensitivities to understand the bet. Use the premium and the underlying level to decide whether you can live with it. The Greek will not fill your order.