Derivative instrument and Put-call parity theory: Difference between pages

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''Risk management - hedging''.
Put-call parity theory links put and call option values via ‘no arbitrage’ market pricing assumptions and the related:
#underlying asset price
#option strike price
#time to maturity and
#theoretically risk-free rate of return.


A derivative instrument or contract is one whose value and other characteristics are derived from those of another asset or instrument (sometimes known as the Underlying Asset).


Derivative instruments are widely used by non-financial corporates for hedging purposes.
So for example if the put option value, underlying asset price, strike price, time to maturity, and risk-free rate of return are known, then the call option value can be calculated using the put-call parity relationship:


Underlying asset price + Put value ''less'' Call value = Present Value of option strike price


<span style="color:#4B0082">'''Example'''</span>
Call value = Underlying asset price + Put value ''less'' Present Value of option strike price


A share option is a type of derivative contract, allowing the holder to buy shares at a certain predetermined strike price.  
In the special case where the strike price of the options is equal to the forward price of the underlying asset, the Put value and the Call value are exactly equal.


The value of the share option derives from the current price of the related underlying share relative to the option strike price.


== Theoretically risk-free portfolios ==
The no-arbitrage pricing relationship is based on the theory that combinations of market assets and liabilities with the same terminal cash flows, must also have the same present values (i.e. the same theoretical current market prices).


== See also ==
For example both the left side and the right side of the put-call parity formula represent portfolios with the same terminal value:
* [[CCR]]
 
* [[Collateral]]
Underlying asset + Put ''less'' Call = Present Value of option strike price
* [[Commodity risk]]
 
* [[CP]]
 
* [[Credit support annex]]
The left side portfolio is built by buying the underlying asset, buying a put option, and selling a call option with the same strike price.
* [[Embedded derivative]]
 
* [[ETD]]
The theoretically risk free terminal value of this portfolio is the equal strike price of the two options.
* [[FC]]
 
* [[Fixing instrument]]
The present value of this left side portfolio is the present value of the strike price.
* [[FVTOCI]]
 
* [[FVTPL]]
 
* [[Hedge fund]]
The right side portfolio is a deposit of cash.
* [[Hedging]]
 
* [[IR]]
This cash portfolio also produces a theoretically risk free terminal value, equal to the strike price of the options.
* [[ISDA Master Agreement]]
 
* [[Margining]]
The current market pricing of these two portfolios must in theory be exactly the same.
* [[Mark to market]]
 
* [[Maturity]]
If this relationship did not hold, there would be an arbitrage opportunity to buy the cheaper portfolio and sell the more expensive one, to earn an immediate risk free profit.
* [[Notional principal]]
* [[Option]]
* [[Outright]]
* [[Potential Future Exposure]]
* [[Replacement cost]]
* [[Risk management]]
* [[Strike price]]
* [[Tracker fund]]
* [[Transfer]]
* [[Underlying]]
* [[Underlying asset]]
* [[Underlying price]]
* [[XVA]]


Therefore market supply and demand pressures will act to quickly re-establish the no arbitrage pricing relationship, following any temporary pricing mis-alignments.


===Other links===
*[http://www.treasurers.org/node/8599  Masterclass: Derivatives, ''Sarah Boyce,'' The Treasurer]


[[Category:Risk_frameworks]]
== See also ==
* [[Arbitrage]]
* [[Interest rate parity]]
* [[Option]]
* [[Parity]]
* [[Put option]]
* [[Risk-free rate of return]]

Revision as of 21:06, 5 February 2018

Put-call parity theory links put and call option values via ‘no arbitrage’ market pricing assumptions and the related:

  1. underlying asset price
  2. option strike price
  3. time to maturity and
  4. theoretically risk-free rate of return.


So for example if the put option value, underlying asset price, strike price, time to maturity, and risk-free rate of return are known, then the call option value can be calculated using the put-call parity relationship:

Underlying asset price + Put value less Call value = Present Value of option strike price

Call value = Underlying asset price + Put value less Present Value of option strike price

In the special case where the strike price of the options is equal to the forward price of the underlying asset, the Put value and the Call value are exactly equal.


Theoretically risk-free portfolios

The no-arbitrage pricing relationship is based on the theory that combinations of market assets and liabilities with the same terminal cash flows, must also have the same present values (i.e. the same theoretical current market prices).

For example both the left side and the right side of the put-call parity formula represent portfolios with the same terminal value:

Underlying asset + Put less Call = Present Value of option strike price


The left side portfolio is built by buying the underlying asset, buying a put option, and selling a call option with the same strike price.

The theoretically risk free terminal value of this portfolio is the equal strike price of the two options.

The present value of this left side portfolio is the present value of the strike price.


The right side portfolio is a deposit of cash.

This cash portfolio also produces a theoretically risk free terminal value, equal to the strike price of the options.

The current market pricing of these two portfolios must in theory be exactly the same.

If this relationship did not hold, there would be an arbitrage opportunity to buy the cheaper portfolio and sell the more expensive one, to earn an immediate risk free profit.

Therefore market supply and demand pressures will act to quickly re-establish the no arbitrage pricing relationship, following any temporary pricing mis-alignments.


See also