Put-call parity theory and Put option: Difference between pages

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Put-call parity theory links put and call option values via ‘no arbitrage’ market pricing assumptions and the related:
1.
#underlying asset price
#option strike price
#time to maturity and
#theoretically risk-free rate of return.


An option which gives the holder the right to <u>sell</u> a specified quantity of a physical underlying asset, such as a commodity, at the strike price specified by the option. The holder will only exercise the option if it is beneficial for the holder to do so, based on the difference between the strike price and the price of the underlying asset at the maturity of the option.


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
2.


Call value = Underlying asset price + Put value ''less'' Present Value of option strike price
A similar option over a non-physical underlying asset.


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.


__NOTOC__
==== Cash settlement ====
In practice many options are cash-settled by a payment, if relevant, by the writer (or seller) of the option to the holder, at the maturity date of the option.


== Theoretically risk-free portfolios ==
There will be a payment if the underlying asset price is favourable for the option holder, compared with the strike price of the option.
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:
Options over non-physical underlying assets are always cash-settled.


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


==== Foreign exchange put options ====
A foreign currency call option is the option to sell a specified quantity of the [[base currency]] in the currency pair, at the strike rate specified in the option.


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.
==== Interest rate options ====
'Lenders' options' hedge against a fall in interest rates.


The present value of this left side portfolio is the present value of the strike price.
For options over [[forward rate agreement]]s, this is a put option.




The right side portfolio is a deposit of cash.
Put options over short-term interest rate [[futures contract]]s are 'borrowers' options'.


This cash portfolio also produces a theoretically risk free terminal value, equal to the strike price of the options.
These hedge against a rise in interest rates.


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 ==
== See also ==
* [[Arbitrage]]
* [[Bear spread]]
* [[Interest rate parity]]
* [[Call option]]
* [[Central bank put]]
* [[Embedded option]]
* [[Option]]
* [[Option]]
* [[Parity]]
* [[Put-call parity theory]]
* [[Put option]]
* [[Risk-free rate of return]]
 
[[Category:Corporate_financial_management]]
[[Category:Financial_risk_management]]

Revision as of 20:40, 14 April 2019

1.

An option which gives the holder the right to sell a specified quantity of a physical underlying asset, such as a commodity, at the strike price specified by the option. The holder will only exercise the option if it is beneficial for the holder to do so, based on the difference between the strike price and the price of the underlying asset at the maturity of the option.


2.

A similar option over a non-physical underlying asset.


Cash settlement

In practice many options are cash-settled by a payment, if relevant, by the writer (or seller) of the option to the holder, at the maturity date of the option.

There will be a payment if the underlying asset price is favourable for the option holder, compared with the strike price of the option.

Options over non-physical underlying assets are always cash-settled.


Foreign exchange put options

A foreign currency call option is the option to sell a specified quantity of the base currency in the currency pair, at the strike rate specified in the option.


Interest rate options

'Lenders' options' hedge against a fall in interest rates.

For options over forward rate agreements, this is a put option.


Put options over short-term interest rate futures contracts are 'borrowers' options'.

These hedge against a rise in interest rates.


See also

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