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LIMITED TIME–THE OPTION GREEKS SIMPLY EXPLAINED BELOW!
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In the pricing of options for derivative contracts, Option Greeks represent a measure of the risk and sensitivity of the option to changes in price. The five Option Greeks are Delta, Gamma, Theta, Vega, and Rho. Each one of these option sensitivity components is explained in detail below. Option Greeks are commonly used in an option pricing calculator known as the Black Scholes model. A link to this calculator can be found here Black-Scholes-Calculator.
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Explanation of the Option Greek Delta:
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Delta can be defined in several ways, depending on your preference. The most commonly used definition is that Delta is the rate of change of the option contract in price relative to the change of the underlying stock price. For instance, if the stock price goes from $22 to $23, then the change in the price of the stock is $1. By how much did your option $23 option contract change? In this example, depending on how long the option has to expiration, the option may have gone from $0.75 to $1.25. In other words, a $0.50 change or a delta of 0.50. So for every $1 change in the price of the stock, the option value will increase by 50 cents. This is the first definition of Delta.
The second commonly used definition for explaining Delta is that Delta is the likelihood or the % probability of an option expiring in-the-money. In the example above, if the option value increased by $0.50, then what Delta is telling you is that the option has a 50 % chance of expiring in-the-money. If the option had increased by $0.75 instead of $0.50, then Delta is telling you that you have a 75 % chance that your position will expire profitably in-the-money. As you can see, Delta is a very useful tool when trading options and knowing how to price them to realize a profit.
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Explanation of the Option Greek Gamma:
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An important piece of information was missing when Delta was explained above. When the stock price moved by $1, the option changed by 50 cents; But what if the stock price increased another dollar to $24. By how much would the option price change then? A little hint, it would not be 50 cents for every dollar move anymore. It would be a slightly higher amount such as $0.60 for every dollar change in the underlying stock price. This is where Gamma comes into play. Gamma is the rate of change of the option’s delta relative to the change in the price of the underlying stock. For example, if the stock rises from $23 to $24 dollars, gamma would be $0.10, which is then added to the old delta of $0.50 to get the new delta of $0.60 for every $1 move in the price of the underlying stock. This addition of gamma to delta continues until delta theoretically becomes 1. This would then mean that for every $1 rise in the price of the underlying stock, your option contract would increase by $1, or a 1 for 1 move! This is the ideal situation when you hold an option contract.
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Explanation of the Option Greek Theta:
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Theta may be the most important Option Greek of them all in that Theta is the one which determines how fast your option will erode in value with the passage of time. Just as a little precaution when buying any option contract, the value of any option value will erode faster and faster the closer the option approaches its expiration day. To rephrase what I just stated, the value of the option will decay exponentially with time until there is no time value left in the price of the option at expiration! only intrinsic value will be left if the option is in-time-money on expiration day, which is the third Friday of every month. So we come to the definition of Theta. Theta is the extrinsic or time value present in the option contract. The longer the option has until expiration, the more valuable the option since the probability of the option expiring profitably is greater as well as the uncertainty of the move of the underlying stock either up or down. In very simple terms, theta is responsible for the day to day decay of the extrinsic or time value part of the option contract. In the same example given above, for every day that passes in the $23 option contract bought at $0.75 per share per contract, theta may decay the value of the option by $0.03 per day, even over the weekend, until there is no time value left in the option contract at expiration Friday. In summary then, the time component of theta is your enemy if you decide to buy an option contract. The reverse is true if you decide to sell an option contract, in which the value of the position increases every day for every day that the underlying stock price stays the same; this strategy of selling an option contract will be discussed in a later post.
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Explanation of the Option Greek Vega:
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In very mundane terms, Vega is the option contract’s sensitivity from its theoretical value to a change in implied volatility. It is usually expressed as a %. For instance, in the example above, if the $23 option contract has an at-the-money implied volatility of 15%, a vega of 0.05, and if the implied suddenly rises to 16% due to increased fear in the marketplace, the value of the option contract will increase 0.05 for every 1% move in implied volatility. So for this example, a rise of 1% will increase the value of the $23 option contract by 0.05. Therefore, the new price of the option will be $0.75 + $0.05 = $0.80. This new value holds true only if the underlying stock price stays stationary at the original price of $22. Two points to consider when working with vega: at-the-money option contracts will have the highest vega value due to uncertainty of where the option price will settle at expiration, since the probability of the underlying stock price making a move either up or down is more or less 50%. The last point to consider about vega is that the longer the option contract has until expiration, the higher will be the sensitivity of the option’s value to a change in implied volatility for the same reason given above—the inherent uncertainty of where the option will settle at expiration Friday.
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Explanation of the Option Greek Rho:
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By far the least important of all the Option Greeks is Rho. Quite simply, rho is the sensitivity of an option’s value to changes in interest rates. If the interest rate rises, the option’s value will rise if it is a call option and its value will fall if it is a put option. The reason for this corresponding rise or fall in the value of the option contract can be understood by speculating what would happen if one bought the underlying stock outright. This would occupy a large amount of capital which could have been earning interest elsewhere if it was not locked up in buying shares of stock. Therefore, the call option’s value must rise if interest rates rise to compensate for this lost interest rate opportunity. Similarly, the value of the put option must fall if interest rates rise since a put is the opposite of a call and is short the stock. If the put is thought of in this way, equivalent share of stock are sold first then bought back later for the profit if the underlying stock price falls in value. This is why a rise in interest rate will affect the price of the put option negatively with a decrease in overall option value. Keep in mind that rho is always positive for calls and negative for puts. That is all you really have to know about rho, and on that note, these then are the five Option Greeks fully explained in all their complexity and beauty.
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