Ancient Greek philosophy, much like the Indian Vedic thought, is unanimously hailed as the mother of deep introspection and radical reasoning. In fact, the European renaissance owes a lot to the Hellenic republic for the knowledge repository in diverse areas including polity, philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric, and aesthetics. No wonder, the Americans still turn to Aristotle’s Poetics to fathom the root cause of any tragedy. The tragic flaw, Aristotle reminds us, is hubris
, an excessive pride that causes the hero to ignore a divine warning or to break a moral law.
In the context of financial tragedies, hubris
could well be the collective complacency and conceit that breed inertia and indecision. Going deeper into the womb of the financial context, a conveniently complacent perception that guides most players in Options trading is that the macro variable of market direction rules the game, with little or no thought to the velocity and volatility of change as also the associated time bleed.
Trust the Greeks for providing a reliable compass to find our way through the often-turbulent, living waters of premium movements – in the form of a lighthouse popularly known as ‘The Option Greeks’. A better appreciation of the Option Greeks will help novice traders lock horns with the intricacies of Options pricing, which go far beyond mere price movements of the underlying stocks or indices and merit a deeper probe into the distinction between option price and option value.
The Option Greeks find their roots in mathematical models like Black-Scholes and Cox-Ross-Rubinstein. They quarantine a given variable to study the effect of its change on the options price. Consequently, we get a concrete rationale, albeit theoretical, to base our trading decisions which otherwise could prove to be a nightmarish experience if driven by blind faith, half-baked advice or reckless choices. If you develop some resonance for the Option Greeks, you would never say, “It’s all Greek to me”. To help you do just that, here’re five Greeks introducing themselves for the very first time in the history of Options Trading:
Delta: Prices change, so do premia
Hi folks, I am well known to students of physics and mathematics. In the context of options trading, I am a dynamic number revealing the change in premium following the change in the price of the underlying security. For call options, I move between 0 and 1. So if I am 0.3, the premium will vary by 0.3 points for every 1 point of change in the underlying price. For Put options, I range between -1 and 0 (diametrically opposite you see). So, for every gain of underlying price, put premium goes down to my extent (exact opposite for any fall in underlying price). By using an options calculator, you can match my values with the given moneyness applied to calls and puts as per the respective logic in contrary directions (ITM: positive intrinsic value and time value, ATM: strike price equal to current price or OTM: no intrinsic value)
Gamma: Who moved my delta
Vega: Left, right, centre of Ups and Downs
Hello, I am expressed as a positive number for both calls and puts, calculated in terms of my 2nd
order derivative Vomma. I let you know the rate at change in the option’s delta in line with the change in the underlying. So, delta moves to the extent of my value for every point move of the underlying. A revised delta is thus original delta + (point change in underlying multiplied by me) I may appear hopelessly vague to you but do pay close attention nevertheless. It’s only when you consult me for risk analysis, you find that equal deltas may not bear identical outcomes. A delta with a higher value of mine will spell higher risk or reward, given the fact that any antagonistic change in the underlying stock or index will have a large adverse effect on the delta (ditto for favourable outcomes).
I measure the rate of change of option’s premium for every percent change in volatility which is in turn represented by fear and uncertainty over likely and unlikely market developments. All options, whether calls or puts, rise in value with the rise in volatility thereby increasing the likelihood of the option expiring ITM. No marks for guessing that I am a positive number, for both calls and puts. All other things being constant, I will always be higher for ATM options compared to the other two variants given that ATM options are most sensitive to volatility in terms of aggregate points. Need I add that OTM options are the most sensitive to volatility in percent terms.
Theta: All about time and its decay
I measure the rate at which an option loses value with the passage of time. As options get closer to expiration, the rate of money loss increases, so does the premium. The eroding premium represents the time decay. Simply put, I represent loss of points in the given time frame. I have different mood swings for different strike prices. For deep OTM and ITM options, I deplete at a furious pace in the initial stages and get reduced to almost nil during the concluding phase. But for ATM options, I do the contrary, constant during the initial periods and super-fast in decay during the last phase, with the pace of deterioration maximum in the last leg. I am the hot favourite of option sellers for obvious reasons. By the way, time expiry is more crucial than what you think. So even if my friend Vega shows high volatility, he may have a limited impact on the option value if the time to expiry is less. So, read mine and Vega’s values in concurrence given that time and volatility are interrelated variables.
Rho: Strictly a matter of interest
I begin (and end) with a humble submission! Yes, I don’t matter much to you given the relatively steady state of bank interest rates. Yet, no harm in knowing me better. I stand for the change in option value for every percent-point change in interest rates. My formula is rather complex, but it should suffice to say that I am calculated as the first derivative of the option's value with respect to the risk-free rate. Interest rates are used in pricing models to consider the options price based on its hedged value. I am positive for calls bought, as higher interest rates push call premiums up. Conversely, I am negative for puts bought as higher interest rates erode put premiums.