Portfolio With Options - Greeks Sensitivity
Put-Call Parity can be chosen as a primary tool for measuring portfolio risk. Not only it can help one to determine portfolio risk, but also to exploit Arbitrage in case it exists when Put-Call Parity equation is violated.
Put-Call Parity in a nutshell is defined as:
Put(K) + Stock - Call(K) = Riskfree Bond ---------------------------(1)
Equation (1) is the heart of the option portfolio so it must be respected at all times. You can think of this equation as a Portfolio Replication such that their market price must match. In case the market prices do not match on both sides of the equation, the arbitrageur can sell the overvalued portfolio and can buy the undervalued portfolio and keep them on books until maturity and collect the risk free cash.
Also, the above scenario assumes that the options are European Style and their maturity is the same as the maturity of the risk free bond, and no dividends will be offered. The result of the above portfolio is to generate the Riskless Cash flow equal to the Strike of the option at expiration.
Let me explain why would it work:
Scenario 1 - Stock Price > Strike Price
Here the short call will be exercised, put will expire worthless, and you WILL BE FORCED to sell the stock at Strike Price
Scenario 2 - Stock Price < Strike Price
Here the short call will expire worthless, put will be exercised, and you WILL sell the stock at Strike Price
Scenario 3 - Stock Price = Strike Price
Here both options will expire worthless and stock will be sold for Strike price which should be same as market price at that moment
So, it must be clear the total payoff in all scenarios will the same amount, the strike price K. Only a Riskfree bond with a maturity value of K can give the same payoff as every other bond will carry risk and your final payoff can be substantially different than K based on other risk factors.
Such portfolios are called Riskless Portfolios, Market Neutral Portfolios, Delta Neutral Portfolio, Riskless Hedged Portfolios and so on. They all mean same thing though that there is no risk if either of these portfolios are held until maturity.
Below table shows a little bit of Options Greeks math to convey the same result that total exposure of the portfolio is 0.
Sorry, don't know why this image is constantly getting rotated but if you don't mind bending your neck, you will truly appreciate the Greeks math behind the portfolio. :). Also, BTW my handwriting is not bad, it's actually the font I am using which might not be the best as per the taste of the reader. :)
I hope you enjoyed reading it.
-Nitin
Put-Call Parity can be chosen as a primary tool for measuring portfolio risk. Not only it can help one to determine portfolio risk, but also to exploit Arbitrage in case it exists when Put-Call Parity equation is violated.
Put-Call Parity in a nutshell is defined as:
Put(K) + Stock - Call(K) = Riskfree Bond ---------------------------(1)
Equation (1) is the heart of the option portfolio so it must be respected at all times. You can think of this equation as a Portfolio Replication such that their market price must match. In case the market prices do not match on both sides of the equation, the arbitrageur can sell the overvalued portfolio and can buy the undervalued portfolio and keep them on books until maturity and collect the risk free cash.
Also, the above scenario assumes that the options are European Style and their maturity is the same as the maturity of the risk free bond, and no dividends will be offered. The result of the above portfolio is to generate the Riskless Cash flow equal to the Strike of the option at expiration.
Let me explain why would it work:
Scenario 1 - Stock Price > Strike Price
Here the short call will be exercised, put will expire worthless, and you WILL BE FORCED to sell the stock at Strike Price
Scenario 2 - Stock Price < Strike Price
Here the short call will expire worthless, put will be exercised, and you WILL sell the stock at Strike Price
Scenario 3 - Stock Price = Strike Price
Here both options will expire worthless and stock will be sold for Strike price which should be same as market price at that moment
So, it must be clear the total payoff in all scenarios will the same amount, the strike price K. Only a Riskfree bond with a maturity value of K can give the same payoff as every other bond will carry risk and your final payoff can be substantially different than K based on other risk factors.
Such portfolios are called Riskless Portfolios, Market Neutral Portfolios, Delta Neutral Portfolio, Riskless Hedged Portfolios and so on. They all mean same thing though that there is no risk if either of these portfolios are held until maturity.
Below table shows a little bit of Options Greeks math to convey the same result that total exposure of the portfolio is 0.
 |
| Option Portfolio Sensitivity |
I hope you enjoyed reading it.
-Nitin
No comments:
Post a Comment