2. Using Delta for Call and Put options
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What are Call and Put Options?
Before we jump into using Delta for Call and Put Options, let’s recap a few important basics for this chapter, shall we?
- Options: Contracts that give the right to buy or sell an amount of an underlying asset at a predetermined price before the contract expires.
- Call Option: This gives the holder the right to buy a stock
- Put Option: This gives the holder the right to sell a stock.
What influences an Option’s price?
To understand how the predetermined price of an option is influenced, let’s take a look at Table 1 below. The table lists the major influences on a call and put option's price. The plus or minus sign indicates an option's price direction resulting from a change in one of the listed variables.
Table 1: Major influence on an Option’s price:
OPTIONS |
Increase in Volatility |
Decrease in Volatility |
Increase in Time to Expiration |
Decrease in time to Expiration |
Increase in the Underlying |
Decrease in the Underlying |
Call |
+ |
- |
+ |
- |
+ |
- |
Put |
+ |
- |
+ |
- |
- |
+ |
Remember that the results will vary in accordance to the time period. If a trader has established a long call option position, there will be a rise in the implied volatility because higher volatility is priced into the option premium. On the other hand, if the trader has established a short call option position, a rise in implied volatility will have an inverse effect.
The writer and and what he wants
Writers are sellers of options. The writer of a naked option ( put or a call), would not benefit from a rise in volatility because writers want the price of the option to decline. When a call option is sold, the writer wants the stock price to remain below the strike price. This is because if the stock's price rose high enough, the seller would have to sell shares to the option holder at the strike price when the market price was higher.
Did you know that sellers of options are paid a premium so that their risks are compensated?
Long and Short Call Options
Let’s take a look at Table 2 and Table 3. Both the tables present the same variables for long and short call options as well as long and short put options.
Table 2: Major influences on a short and long call option’s price.
OPTIONS |
Increase in Volatility |
Decrease in Volatility |
Increase in Time to Expiration |
Decrease in time to Expiration |
Increase in the Underlying |
Decrease in the Underlying |
long Call/put |
+ |
- |
+ |
- |
+ |
- |
Short call/put |
- |
+ |
- |
+ |
- |
+ |
Notice how a decrease in implied volatility, reduced time to expiration, and a fall in the price of the underlying security will benefit the short call holder. On the other hand, an increase in volatility, a greater time remaining on the option, and a rise in the underlying will benefit the long call holder.
Long and Short Put Options
Table 3: Major influences on a short and long put option’s price.
OPTIONS |
Increase in Volatility |
Decrease in Volatility |
Increase in Time to Expiration |
Decrease in time to Expiration |
Increase in the Underlying |
Decrease in the Underlying |
Long call/put |
+ |
- |
+ |
- |
- |
+ |
Short call/put |
- |
+ |
- |
+ |
+ |
- |
Notice how a short put holder benefits from a decrease in implied volatility, a reduced time remaining until expiration, and a rise in the price of the underlying security, while a long put holder benefits from an increase in implied volatility, a greater time remaining until expiration, and a decrease in the price of the underlying security.
The Role of Interest Rates
It is interesting to note that interest rates play a negligible role in a position during the life of most option trades. However, the Greek rho, measures the impact of changes in interest rates on an option's price. Usualty, higher interest rates make call options more expensive and put options less expensive, considering that all other things are equal.
Wrapping up
All of the above provides context for an examination of the risk categories used to gauge the relative impact of these variables. Keep in mind that the Greeks help traders to project changes in an option's price.
A quick recap
- Options: Contracts that give the right to buy or sell an amount of an underlying asset at a predetermined price before the contract expires.
- Call Option: This gives the holder the right to buy a stock
- Put Option: This gives the holder the right to sell a stock.
- When a call option is sold, the writer wants the stock price to remain below the strike price.
- A decrease in implied volatility, reduced time to expiration, and a fall in the price of the underlying security will benefit the short call holder.
- An increase in volatility, a greater time remaining on the option, and a rise in the underlying will benefit the long call holder.
- A short put holder benefits from a decrease in implied volatility, a reduced time remaining until expiration, and a rise in the price of the underlying security.
- A long put holder benefits from an increase in implied volatility, a greater time remaining until expiration, and a decrease in the price of the underlying security.
- interest rates play a negligible role in a position during the life of most option trades.
- The Greek rho measures the impact of changes in interest rates on an option's price.
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