American put call parity with dividends

Free Investment Banking Tutorials WallStreetMojo. By Dheeraj Vaidya Leave a Comment Filed Under: Put-Call Parity — As the name suggests, put-call parity establishes a relationship between put options and call options price. It is defined as a relationship between the prices of a European put options and calls options having same strike prices, expiry and underlying or we can define it as an equivalence relationship between the Put and Call options of a common underlying carrying the same strike price and expiry.

Put-Call parity theorem says that premium price of a call options implies a certain fair price for corresponding put options provided the put options has the same strike price, underlying and expiry and vice versa.

It also shows the three sided relationship between a call, a put and an underlying security. Before going further into in-depth study of put-call parity, first get an insight view of certain terminologies and definitions related to options.

Impact on Portfolio A in Scenario 1: Portfolio A will be worth the zero coupon bond i. Therefore, portfolio A will be worth the stock price S T at time T.

Impact on Portfolio A in Scenario 2: Portfolio A will be worth the share price i. Hence, portfolio A will be worth stock price S T at time T.

Impact on Portfolio B in Scenario 1: Portfolio B will be worth the stock price or share price i. Therefore, portfolio B will be worth the stock price S T at time T. Impact on Portfolio B in Scenario 2: Portfolio B will be worth the difference between strike price and stock price i. Hence, portfolio B will be worth strike price X at time T.

In the above table we can summarize our findings that when stock price is more than the strike price X , the portfolios are worth the stock or share price S T and when the stock price is lower than the strike price, the portfolios are worth the strike price X. In other words, both the portfolios are worth max S T , X.

Since, both the portfolios have identical values at time T, they must therefore have similar or identical values today since the options are European, it cannot be exercised prior to time T. And if this is not true an arbitrageur would exploit this arbitrage opportunity by buying the cheaper portfolio and selling the costlier one and book an arbitrage risk free profit.

Now, as per the above equation of put-call parity, value of the combination of call option price and the present value of strike would be,. Here, we can see that first portfolio is overpriced and can be sold an arbitrageur can create a short position in this portfolio and second portfolio is relatively cheaper and can be bought arbitrageur can create a long position by the investor in order to exploit arbitrage opportunity.

This arbitrage opportunity involves buying a put option and a share of the company and selling a call option.

Hence, the repayment amount would be. Hence, the net profit generated by the arbitrageur is. Here, the left side of the equation is called Fiduciary Call because in fiduciary call strategy, an investor limits its cost associated with exercising the call option as to fee for subsequently selling an underlying which has been physical delivered if the call is exercised.

In case, share prices goes up the investor can still minimizes their financial risk by selling shares of the company and protects their portfolio and in case the share prices goes down he can close his position by exercising the put option.

In this case, the investor will not exercise its put option as the same is out of the money but will sell its share at current market price CMP and earn the difference between CMP and initial price of stock i.

Had the investor not been purchased sock along with the put option, he would have been end up incurring loss of his premium towards option purchase. So far in our studies, we have assumed that there is no dividend paid on the stock. Therefore, the very next thing which we have to take into consideration is impact of dividend on put-call parity. Since interest is a cost to an investor who borrows funds to purchase stock and benefit to investor who shorts the stock or securities by investing the funds.

Here we will examine how the Put-Call parity equation would be adjusted if stock pays dividend. Also, we assume that dividend which is paid during the life of the option is known.

Here, the equation would be adjusted with the present value of dividend. And along with call option premium, the total amount to be invested by the investor is cash equivalent to present value of zero coupon bond which is equivalent to strike price and present value of dividend.

Put-Call Parity | Formula | Example | Dividends | Arbitrage

Here, we are making adjustment in fiduciary call strategy. The adjusted equation would be. We can adjust the dividends in other way also which will yield the same value.

The only basic difference between these two ways are while in first one we have added the dividends amount in strike price, in the other one we have adjusted the dividends amount directly from the stock. In the above formula we have deducted the dividends amount PV of dividends directly from the stock price.

Your email address will not be published. CFA Institute does not endorse, promote, or warrant the accuracy or quality of WallStreetMojo.

Skip links Skip to primary navigation Skip to content Skip to primary sidebar Free Investment Banking Tutorials WallStreetMojo. Call Options and Put Options Before going further into in-depth study of put-call parity, first get an insight view of certain terminologies and definitions related to options.

Call option is a derivative contract which gives owner the right but not the obligation to buy an underlying asset at a predetermined price strike price and time till expiration of the contract. The call options is generally exercised by holder only if the stock price is more than the strike price or the options is in the money ITM. It is logical not to exercise if the option is out of the money OTM. And hence, the pay-off for call option is max S T -X,0.

Put option gives owner the right but not the obligation to sell an underlying asset at a predetermined price and time till expiration of the contract. The put options is generally exercised by holder only if the stock price is less than the strike price. And hence, the pay-off for put option is max X- S T ,0. Put-Call Parity Example The above mentioned theorem can be elaborated with the below example.

Likewise, for portfolio B, we will analyze the impact with both the scenarios.

The above pay-offs are summarized below in Table 1. Leave a Reply Cancel reply Your email address will not be published. Search Search this website. Topics Investment Banking 98 Equity Research 76 CFA 33 Financial Modeling 20 Accounting 84 Certifications 86 FRM 13 Valuation 32 Finance Careers 47 Alternative Investments 25 Derivatives 17 Fixed Income 13 Recommended Books 55 Trading What is Investment Banking?

Financial Modeling Training Equity Research Private Equity Analyst What is Hedge Fund? Option Trading Strategies Alibaba IPO Financial Model Leveraged Buyout Analysis CAPM Beta Earnings Per Share Terminal Value Free Cash Flow to Firm Comparable Comp Analysis Box IPO Valuation. CFA Exam FRM Exam PRM Examination CFA vs FRM - Which is Better? CPA vs CFA - Which is Better? Claritas vs CFA Exam ACCA vs ACA - What's the Difference?

CFA vs MBA ACCA vs CIMA CPA vs CA CA vs CS. After six months, if share price is more than the strike price, call option would be exercised and if it is below strike price then put option would be exercised.