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miércoles, 1 de octubre de 2014

The Options Premium

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The symmetry of rights and obligations that exists in futures contracts where two parties agree to make a purchase/sale of an underlying asset when the contract reach maturity, ceases to apply in the options because one party (the buyer of the option ) has the right but not the obligation to buy (call) or sell (put), while the seller or writer of the option will only be required to sell (call) or purchase (put) the underlying.


Call optionSell option
Option buyerRight to buyRight to sell
Option sellerObligation to sellObligation to buy
This difference of rights and obligations creates the existence of the premium. The premium can be defined as the price of the option, or what is the same, the cost of the option for the buyer. The buyer of the option pays the premium and the option seller collects the premium.

The premium is comprised of intrinsic value plus the time value and volatility, which are components that are described below:
  • Intrinsic Value: The value of the option if exercised at the time of assessment. Thus, Call options will have positive intrinsic value if  their strike price is below the current price of the underlying asset (the option buyer can buy at a lower price) while the PUT options will have positive intrinsic value if the strike price is about the current price of the underlying asset (the option buyer can sell at a higher price).
  • Time Value: The amount of the premium that exceeds the intrinsic value of the option. Time value (also known as extrinsic value) is maximum for ATM options and decays over time. The time value of an option is directly related to how much time an option has until expiration and is approximately the same for call and put options with the same strike price.
  • Volatility: Is the implied volatility of the underlying asset.
The premium also depends on the strike price, which is the price at which the option´s buyer is able to buy or sell the underlying asset of the option if the contract right is exercised. Also, as the option nears its expiration date, the time value will edge closer and closer to zero.

In exchange for the premium, the seller of a put option is obligated to buy the asset if the buyer exercises the option. Symmetrically, the buyer of a put would be entitled (if they exercise the option) to sell the underlying at the established conditions. In the case of a call option, the buyer has the right to buy the underlying in exchange for payment of a premium, and the option writer has the obligation to sell the underlying. The option seller collects the premium always, regardless of whether or not the buyer exercises the option.

The option premium is negotiated according to the law of supply and demand whic is set by the market. However, there are theoretical models that attempt to determine the price of the option based on a number of parameters: 
  • Price of underlying asset 
  • Strike price 
  • Interest rate 
  • Dividends payable (only in stock options). 
  • Time to expiration 
  • Future volatility

Influence of interest rates on option prices 

  • A rise in interest rates causes a decline in the price of a put option. 
  • A rise in interest rates causes an increase in the price of the call option. 
In general, changes in interest rates have no significant influence on the price of options, so that, in practice, are not taken into consideration.

Influence of rising volatility in the price of the  

  • The increase in volatility causes an increase in the price of the option, both call and put options. 
  • The lower volatility causes the opposite effect, that is, the decrease of its price.



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