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The Valuation of Options

Valuing Options

As we said before, options themselves have a value.  Remember that options are totally separate entities to the underlying assets from which they are derived (hence the term derivative).  But in themselves they do have a value, which can be split into two parts:

  1. Intrinsic Value; and
  2. Time Value

In general:

  • Intrinsic Value is that part of the option's value which is In the Money (ITM).
  • Time Value is the remainder of the option's value.  Out of the Money (OTM) options will have no Intrinsic Value, and their price will solely be based on Time Value.  Time Value is another way of say Hope Value.  This hope is based on the amount of time left to Expiration and the price of the underlying asset, the hope being the possibility of additional (profitable) price movement in the underlying security.
  • Time Value is subject to Time Decay.  Time Decay increases exponentially in the last 30 days before expiration.

ITM, OTM and At the Money (ATM) Calls

  • ITM where the current stock price is above the call strike price
  • ATM where the current stock price is equal to or near to the call strike price
  • OTM where the current stock price is below the call strike price

ITM, OTM and ATM Puts

  • ITM where the current stock price is below the put strike price
  • ATM where the current stock price is equal to or near to the put strike price
  • OTM where the current stock price is above the put strike price

Intrinsic and Time Value for Calls - Example 1: ITM

Call Intrinsic Value Call Time Value
Stock Price $56.00 Stock Price $56.00
Call Premium $7.33 Call Premium $7.33
Exercise Price $50.00 Exercise Price $50.00
Time to Expiration 2 months Time to Expiration 2 months
Intrinsic Value $56.00 - $50.00 = $6.00 Time Value $7.33 - $6.00 = $1.33

Notice how [Intrinsic Value + Time Value] = the Option Value

Formulae for Intrinsic and Time Values for Calls:

  • Call Intrinsic Value = Stock Price - Exercise Price
  • Call Time Value = Call Premium - Call Intrinsic Value

The minimum Intrinsic Value is zero.

Intrinsic and Time Value for Calls - Example 2: OTM

Call Intrinsic Value Call Time Value
Stock Price $48.00 Stock Price $48.00
Call Premium $0.75 Call Premium $0.75
Exercise Price $50.00 Exercise Price $50.00
Time to Expiration 2 months Time to Expiration 2 months
Intrinsic Value $48.00 - $50.00 = $0.00 Time Value $0.75 - $0.00 = $0.75

Notice how [Intrinsic Value + Time Value] = the Option Value

Formulae for Intrinsic and Time Values for Calls:

  • Call Intrinsic Value = Stock Price - Exercise Price
  • Call Time Value = Call Premium - Call Intrinsic Value

The minimum Intrinsic Value is zero.

Intrinsic and Time Value for Puts - Example 3: ITM

Put Intrinsic Value Put Time Value
Stock Price $77.00 Stock Price $77.00
Put Premium $5.58 Put Premium $5.58
Exercise Price $80.00 Exercise Price $80.00
Time to Expiration 4 months Time to Expiration 4 months
Intrinsic Value $80.00 - $77.00 = $3.00 Time Value $5.58 - $3.00 = $2.58

Notice how [Intrinsic Value + Time Value] = the Option Value

Formulae for Intrinsic and Time Values for Puts:

  • Put Intrinsic Value = Exercise Price - Stock Price
  • Put Time Value = Put Premium - Put Intrinsic Value

The minimum Intrinsic Value is zero.

Intrinsic and Time Value for Puts - Example 4: OTM

Put Intrinsic Value Put Time Value
Stock Price $85.00 Stock Price $85.00
Put Premium $1.67 Put Premium $1.67
Exercise Price $80.00 Exercise Price $80.00
Time to Expiration 4 months Time to Expiration 4 months
Intrinsic Value $80 - $85.00 = $0.00 Time Value $1.67 - $0.00 = $1.67

Notice how [Intrinsic Value + Time Value] = the Option Value

Formulae for Intrinsic and Time Values for Puts:

  • Put Intrinsic Value = Exercise Price - Stock Price
  • Put Time Value = Put Premium - Put Intrinsic Value

The minimum Intrinsic Value is zero.

The 7 Factors affecting the Pricing of Options Premiums

  1. Type of option (call or put)
  2. The current Price of the underlying asset
  3. The Exercise (Strike) Price
  4. Time remaining to Expiration
  5. Volatility of the underlying asset
  6. The Dividend payable on the underlying asset
  7. Current Interest Rates (the risk free 90 day T-Bill rate)

Put / Call Parity Explained

Call prices, Put prices and the associated asset prices are all related to each other.  This must be the case or else professional traders would be able to arbitrage (make risk free trades).

Put-call parity is a fundamental relationship that must exist between the prices of a put option and call option if both have the same underlying asset, Strike Price and Expiration Date.

The Put-call parity model is based on expiration date investment values associated with 4 different securities:

  1. A call option;
  2. A put option with identical terms;
  3. The underlying asset for the above call and put;
  4. A risk-free security with the same maturity date as the options' Expiration Date and with an expiration payoff equal to the options' Strike Price.

Put-call parity is used for 2 purposes:

  1. To value a call option relative to a put with identical terms.
  2. To show how the Expiration Date payoffs on any one of these 4 securities can be replicated by taking appropriate positions in the other 3 securities (ie creating synthetic positions).