An overview of option Greeks — The Delta, Theta and Vega of options pricing theory
Author : Nupur Pavan Bang/DNA
Content :
Content :
Walking down eat street, lost in thoughts of Hari Puttar (the greatest wizard of all times), Monsoon bumps into her friend Nicky, once neighbour and now a professor of finance at a business school.
She delightedly said, “Hey Nicky, I have been hunting for you for the past few months. I had a strange dream on one of those nights when I went off to sleep while reading Hari Puttar and the Quarter Muscle King.
I saw some ghosts in a graveyard, discussing a ghostly contract known as options. It sure looked like a great financial discovery, which could be used to make humongous amounts of money on the stock markets, at low risk.
I brushed off the dream thinking that I have been reading too much about wizards and broomsticks and shadows. But lo-behold, just a few days later, my security analysis professor at the B-school started teaching us derivatives! It was, as though, I was reliving my dream in the class.
The ghosts sure were absolutely right. But, what I learnt in the class is that one has to pay a premium to acquire an option.
The premium is calculated based on some scary looking models namely the Black-Scholes Model or the Binomial Option Pricing Model.
However, the option premium is not constant. It keep changing like the share prices. Now I am puzzled. Why do the premiums change? What are the factors that affect the price of the option contacts? When I asked my professor about it, she said, “It’s not in your syllabus.”
My interest is piqued by the wonderful world of options. And who else is better than you at explaining the nuances of derivative products?”
Pleased to meet Monsoon, Nicky thinks, “Some things never change. And one of them is the non-stop chattering of Monsoon.” Having been declared an expert on derivatives, Nicky is all enthusiastic about clearing Monsoon’s doubts.
She chuckles, “You are absolutely right. The option premium keeps changing due to changes in various factors like the volatility of the underlying asset, the time to maturity of the contract, the risk free rate and the price of the underlying asset.”
Monsoon looks lost and says, “Nicky, it all seems Greek to me. Can you speak in plain English?” Nicky laughs at the unintended pun. “You are right Monsoon. It is indeed called the Greeks. The changes in option premiums with changes in variables that affect the premiums are known as the Greeks.”
Monsoon looks further lost. Nicky explains, “When the price of the underlying asset increases, the price of a call option will increase, and the price of a put option will fall. The sensitivity of option price to a change in the price of the underlying is measured by Delta. Similarly, when interest rates rise, the value of the call option rises as the opportunity cost of buying stocks will be higher due to high borrowing cost.”
Monsoon begins to understand how the option premiums change due to changes in various variables.
She nods at Nicky in complete understanding and poses another question, “How about the time to expiration and the volatility of the underlying stocks? How do they affect the premium?”
Nicky is ready as usual, “If the time of maturity, or the expiration period of the option contract, is increased, the premiums will increase as the writer of the option will have to bear the risk for a longer period and the writer would want to be compensated for the time value of money. This is measured by Theta.”
Nicky further explains, “Monsoon, as you know, the primary objective of options is to ascertain a certain amount of cash flows at some time in the future. Traders and investors use options extensively to hedge the risk of changing prices in the spot market.
Thus, higher the changes in price of an asset, greater will be the demand for option contracts. That is, the greater the volatility of the underlying asset, the higher will be the option premium. The sensitivity of option premiums to changes in volatility is measured by Vega.”
Monsoon is not satisfied. She has another question, “Will the premiums for both call and put options be higher with higher time to maturity and higher volatility of the underlying asset?”
Nicky is pleased that Monsoon’s thoughts are going on the right track, says, “You are absolutely right. Both call and put option will be more valuable when the time to maturity is higher and the volatility of the underlying asset is higher.”
Before Monsoon could pose another question, Nicky quickly added, “Now that you know about Delta, Theta and Vega, let me tell you something about Gamma too. Gamma is the sensitivity of the delta with respect to changes in underlying asset prices. This means that Gamma is a second order derivative. Higher the gamma, higher is the risk of changes in option premium due to changes in prices of the underlying.”
Monsoon finally breathes easy. She has finally learnt the meaning of the Greeks. Just as she is fascinated by Hari Puttar and his world of magic, she is awestruck by options and the world of Greeks.
She profusely thanks Nicky and as usual begins to fill in Nicky with
all the gossip in the colony from where Nicky had moved out after being
offered a house at the university
campus.
She delightedly said, “Hey Nicky, I have been hunting for you for the past few months. I had a strange dream on one of those nights when I went off to sleep while reading Hari Puttar and the Quarter Muscle King.
I saw some ghosts in a graveyard, discussing a ghostly contract known as options. It sure looked like a great financial discovery, which could be used to make humongous amounts of money on the stock markets, at low risk.
I brushed off the dream thinking that I have been reading too much about wizards and broomsticks and shadows. But lo-behold, just a few days later, my security analysis professor at the B-school started teaching us derivatives! It was, as though, I was reliving my dream in the class.
The ghosts sure were absolutely right. But, what I learnt in the class is that one has to pay a premium to acquire an option.
The premium is calculated based on some scary looking models namely the Black-Scholes Model or the Binomial Option Pricing Model.
However, the option premium is not constant. It keep changing like the share prices. Now I am puzzled. Why do the premiums change? What are the factors that affect the price of the option contacts? When I asked my professor about it, she said, “It’s not in your syllabus.”
My interest is piqued by the wonderful world of options. And who else is better than you at explaining the nuances of derivative products?”
Pleased to meet Monsoon, Nicky thinks, “Some things never change. And one of them is the non-stop chattering of Monsoon.” Having been declared an expert on derivatives, Nicky is all enthusiastic about clearing Monsoon’s doubts.
She chuckles, “You are absolutely right. The option premium keeps changing due to changes in various factors like the volatility of the underlying asset, the time to maturity of the contract, the risk free rate and the price of the underlying asset.”
Monsoon looks lost and says, “Nicky, it all seems Greek to me. Can you speak in plain English?” Nicky laughs at the unintended pun. “You are right Monsoon. It is indeed called the Greeks. The changes in option premiums with changes in variables that affect the premiums are known as the Greeks.”
Monsoon looks further lost. Nicky explains, “When the price of the underlying asset increases, the price of a call option will increase, and the price of a put option will fall. The sensitivity of option price to a change in the price of the underlying is measured by Delta. Similarly, when interest rates rise, the value of the call option rises as the opportunity cost of buying stocks will be higher due to high borrowing cost.”
Monsoon begins to understand how the option premiums change due to changes in various variables.
She nods at Nicky in complete understanding and poses another question, “How about the time to expiration and the volatility of the underlying stocks? How do they affect the premium?”
Nicky is ready as usual, “If the time of maturity, or the expiration period of the option contract, is increased, the premiums will increase as the writer of the option will have to bear the risk for a longer period and the writer would want to be compensated for the time value of money. This is measured by Theta.”
Nicky further explains, “Monsoon, as you know, the primary objective of options is to ascertain a certain amount of cash flows at some time in the future. Traders and investors use options extensively to hedge the risk of changing prices in the spot market.
Thus, higher the changes in price of an asset, greater will be the demand for option contracts. That is, the greater the volatility of the underlying asset, the higher will be the option premium. The sensitivity of option premiums to changes in volatility is measured by Vega.”
Monsoon is not satisfied. She has another question, “Will the premiums for both call and put options be higher with higher time to maturity and higher volatility of the underlying asset?”
Nicky is pleased that Monsoon’s thoughts are going on the right track, says, “You are absolutely right. Both call and put option will be more valuable when the time to maturity is higher and the volatility of the underlying asset is higher.”
Before Monsoon could pose another question, Nicky quickly added, “Now that you know about Delta, Theta and Vega, let me tell you something about Gamma too. Gamma is the sensitivity of the delta with respect to changes in underlying asset prices. This means that Gamma is a second order derivative. Higher the gamma, higher is the risk of changes in option premium due to changes in prices of the underlying.”
Monsoon finally breathes easy. She has finally learnt the meaning of the Greeks. Just as she is fascinated by Hari Puttar and his world of magic, she is awestruck by options and the world of Greeks.
She profusely thanks Nicky and as usual begins to fill in Nicky with
all the gossip in the colony from where Nicky had moved out after being
offered a house at the university
campus.
The author is a member of ACCA, UK and a faculty member at ICFAI Business School, Hyderabad and can be reached at npbang@gmail.com
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