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:

Intrinsic Value; and

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 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 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
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.
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.
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.
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.

Type of option (call or put)

The current Price of the underlying asset

The Exercise (Strike) Price

Time remaining to Expiration

Volatility of the underlying asset

The Dividend payable on the underlying asset

Current Interest Rates (the risk free 90 day TBill rate)
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).
Putcall 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 Putcall parity model is based on expiration date investment values associated
with 4 different securities:

A call option;

A put option with identical terms;

The underlying asset for the above call and put;

A riskfree security with the same maturity date as the options' Expiration Date and
with an expiration payoff equal to the options' Strike Price.
Putcall parity is used for 2 purposes:

To value a call option relative to a put with identical terms.

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).