Equivalence and Put-call parity theory: Difference between pages

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''European Union (EU) regulation.''
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.


In certain cases the EU may recognise that a non-EU legal, regulatory and/or supervisory regime is 'equivalent' to the corresponding EU framework.


That recognition, in turn, means authorities in the EU may rely on supervised entities’ compliance with the equivalent non-EU framework, and allow the entity to operate more freely than it might otherwise be able to (without equivalence).
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:


This approach is designed to bring benefits to both the EU and third-country financial markets.
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


The significance of the equivalence concept, for UK financial services, is that the UK might choose, post-Brexit, to keep its regulatory regime closely aligned with the EU regime, in order to benefit from the possibility of equivalence.
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.




<span style="color:#4B0082">'''''Equivalence recognition unlikely'''''</span>
== 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).


:"In addition to disrupting supply chains, Brexit has caused some fragmentation of banking activity for corporates.
For example both the left side and the right side of the put-call parity formula represent portfolios with the same terminal value:


:It seems increasingly unlikely that we shall see ‘equivalence’ recognition for UK/EU financial services that were not covered by the Trade & Cooperation Agreement.
Underlying asset + Put ''less'' Call = Present Value of option strike price


:Treasurers will want to monitor the expiry dates (some in 2022) of various temporary permissions that came into effect post-Brexit, and to ask their banks whether there may be any implications for corporate clients."


:''The Treasurer magazine, Issue 4, 2021, p31 - Treasury in 2022.''
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.


<span style="color:#4B0082">'''''Equivalence and passporting'''''</span>
The present value of this left side portfolio is the present value of the strike price.


:"In brief, equivalence is the willingness of one regulator to accept that another regulator's rules achieve the same regulatory outcomes as their own, and so some element of cross-border activity can be allowed.


:Equivalence must be agreed, but is subject to negotiation, market by market.
The right side portfolio is a deposit of cash.


:Passporting is the acceptance that once permitted to trade in one state, a business can trade in another without further compliance requirements."
This cash portfolio also produces a theoretically risk free terminal value, equal to the strike price of the options.


:''The Treasurer magazine, March 2017, p12 - Technical briefing.''
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.


== See also ==
Therefore market supply and demand pressures will act to quickly re-establish the no arbitrage pricing relationship, following any temporary pricing mis-alignments.
* [[Brexit]]
* [[EU-UK Trade and Cooperation Agreement]]
* [[European Economic Area]]
* [[European Union ]]
* [[Free movement of labour]]
* [[Gold-plating]]
* [[Harmonisation]]
* [[Passporting]]
* [[Prudential Regulation Authority]]
* [[Schengen Area]]
* [[Single Market]]




== Other links ==
== See also ==
[https://ukandeu.ac.uk/rethinking-uk-financial-services-regulation-after-brexit/ Rethinking UK financial services regulation after Brexit, UK in a Changing Europe, December 2020]
* [[Arbitrage]]
 
* [[Interest rate parity]]
[https://www.instituteforgovernment.org.uk/explainers/future-relationship-equivalence UK-EU future relationships: options for equivalence, Institute for Government, February 2020]
* [[Option]]
 
* [[Parity]]
[[Category:Accounting,_tax_and_regulation]]
* [[Put option]]
[[Category:The_business_context]]
* [[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