Put-call parity is an important principle in options pricing first identified by Hans Stoll in his paper, The Relation Between Put and Call Prices, in 1969.
Put call parity describes the relation between European calls and puts of the same underline security, with the same expiration and strike price. So, the call premium plus the strike price equals the put premium plus the current stock price.
The above relation tells us that a long put is equal to a long call and the short selling of the stock (minus sign in front of S). An option is a contract that gives a person or institution the right to buy or sell an asset at a specified price. This spreadsheet uses the Put Call Parity relation, Binomial Option Pricing and Black Scholes model to value options. The Put Call Parity assumes that options are not exercised before expiration day which is a necessity in European options. The spreadsheet supports the calculation of the Stock Price, Put Price, Present value of Strike Price or Call Price depending on the input values provided.
For many years, financial analysts have difficulty in developing a rigorous method for valuing options. This worksheet sets up a replicating portfolio by borrowing money at the risk free rate and purchasing an amount of the actual stock to replicate the payoff of the Call Option.
This worksheet sets up a replicating portfolio by lending money at the risk free rate and selling an amount of the actual stock to replicate the payoff of the Put Option.
Note - If you are the user of a previous version (of the Professional Options Valuation package), please contact us for your free upgrade. In general, the value of a put option implies a fair value for the corresponding call, and vice versa. From a trading perspective, the put-call parity reveals an arbitrage opportunity if there is a divergence between the value of calls and puts in the same category--in other words, if the parity is violated. Isolating American Capital Agency Corp's Dividend With Options - American Capital Agency Corp.


A call option is a contract to buy an asset at a fixed price while a put option is a contract to sell an asset at a fixed price. It defines a relationship between the price of a call option and a put option with the same strike price and expiry date, the stock price and the risk free rate.
This is until Fisher Black and Myron Scholes published the article "The Pricing of Options and Corporate Liabilities" in 1973 to describe a model for valuing options. It then calculates the value (price) of the Call Option through observing the value of the portfolio. It then calculates the value (price) of the Put Option through observing the value of the portfolio. The Binomial Option Pricing assumes two possible values of the stock price at the end of the period (maturity). The put-call parity explains the relationship between the prices of put and call options in the same category--in other words, options with the same strike price, expiration date and underlying price. Thus, the price of one option cannot move very far without the price of the corresponding option changing accordingly. If an option pricing model that produces put and call prices does not satisfy the parity, it can open up arbitrage opportunities. The parity is violated when there is a large price difference between the put and call options. Although the parity concept is strictly confined to European options, the relationship is applicable to American options as well (adjusting for dividends and interest rates). Although arbitrage strategies are not considered useful for the average trader, the corresponding synthetic relationship in the options market can reveal trading strategies. The book led me to thinking about a company I had written previously about, American Capital Agency Corp.
Conversion and reversal strategies are the most commonly used arbitrage techniques that profit from the put-call parity. Basically, the Binomial Option Pricing and Black Scholes models use the simple idea of setting up a replicating portfolio which replicates the payoff of the call or put option.


The Black Scholes Model provides a formula for calculating the value of the option (or portofolio) in the situation above and thus allows us to easily value options. Not to imply there is anything improper transpiring at the company, but rather to think of a way to isolate the dividend and protect a portfolio from any losses due to an unforeseen event occurring at the company, as similar to American Capital, Allied attracted investors seeking dividends. The American type option can be exercised any time up to the expiration date whereas the European type of option can only be exercised on the expiration date.
One important usage of option is to adjust the risk exposure an investor has to the underlying assets. The American Capital option chain for January 2013 expiration date is as follows: (Click to enlarge) Due to the high dividend, the put options are much more expensive than the call options. This relates to the theory of Put-Call Parity, which is as follows: This formula ensures there are no arbitrage opportunities, but for our purposes I'm utilizing it to demonstrate that dividends cause a put option to be worth more.
To insure against the price collapse, I would utilize the put options with a strike of $25, costing $4.21. Essentially, to put this trade on, you have to conclude that there is less than a 1 in 3 chance that American Capital cuts the dividend over the next year- but still a chance- or you wouldn’t bother with the hedge. The payoff and risk both for enacting this strategy and not enacting this strategy graphically: (Click to enlarge) Due to the unique economic environment we currently operate in and the business fundamentals of American Capital that I laid out in my previous article on the company, I continue to see this security offering an excellent opportunity for those seeking an above average yield. Further declines would affect the amount of cash American Capital generates as short term yields are unlikely to go anywhere over the next year. If the long term bond rates begin to rise again and you decide you want to exit the hedge, you can always sell the put and recover much of its value, as the Theta (time value) of a put option doesn’t drop off dramatically until closer to expiry.
Although the Vega (volatility) could have an additional positive or negative effect on the call option, depending on the timing of your exit. Luis Goncalves-Pinto, a researcher at the National University of Singapore, for this as well as other ideas with regards to options.



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