Why does put call parity hold

To achieve higher returns in the stock market, besides doing more homework on the companies you wish to buy, it is often necessary to take on higher risk. A most common way to do that is to buy stocks on margin Day trading options can be a successful, profitable strategy but there are a couple of things you need to know before you use start using options for day trading Learn about the put call ratio, the way it is derived and how it can be used as a contrarian indicator 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 It states that the premium of a call option implies a certain fair price for the corresponding put option having the same strike price and expiration date, and vice versa In options trading, you may notice the use of certain greek alphabets like delta or gamma when describing risks associated with various positions.

They are known as "the greeks" Since the value of stock options depends on the price of the underlying stock, it is useful to calculate the fair value of the stock by using a technique known as discounted cash flow Risk Warning: Stocks, futures and binary options trading discussed on this website can be considered High-Risk Trading Operations and their execution can be very risky and may result in significant losses or even in a total loss of all funds on your account.

You should not risk more than you afford to lose. Before deciding to trade, you need to ensure that you understand the risks involved taking into account your investment objectives and level of experience. Information on this website is provided strictly for informational and educational purposes only and is not intended as a trading recommendation service. The Options Guide. Also, after six months, either the put or call option would be in the money In The Money The term "in the money" refers to an option that, if exercised, will result in a profit.

It varies depending on whether the option is a call or a put. A call option is "in the money" when the strike price of the underlying asset is less than the market price. A put option is "in the money" when the strike price of the underlying asset is more than the market price.

Hence, the net profit generated by the arbitrageur is. Put-Call parity theorem only holds true for European style options as American style options can be exercised at any time prior to its expiry. 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 the fee for subsequently selling an underlying which has been physically delivered if the call is exercised.

In case of share prices go up, the investor can still minimize their financial risk Financial Risk Financial risk refers to the risk of losing funds and assets with the possibility of not being able to pay off the debt taken from creditors, banks and financial institutions.

A firm may face this due to incompetent business decisions and practices, eventually leading to bankruptcy. 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 the current market price CMP and earn the difference between CMP and the initial price of stock i.

Had the investor not been purchased sock along with the put option, he would have been ended up incurring the loss of his premium towards option purchase. What would be the premium for the put option assuming a risk-free rate Risk-free Rate A risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds.

Although, it does not exist because every investment has a certain amount of risk. 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 the impact of dividend on put-call parity. Since interest is a cost to an investor who borrows funds to purchase stock and benefit to the 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 the stock pays a 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 the dividend. And along with the call option premium, the total amount to be invested by the investor is cash equivalent Cash Equivalent Cash equivalents are highly liquid investments with a maturity period of three months or less that are available with no restrictions to be used for immediate need or use.

Let us begin by defining arbitrage and how arbitrage opportunities serve the markets. Arbitrage is, generally speaking, the opportunity to profit arising from price variances on one security in different markets. For example, if an investor can buy XYZ in one market and simultaneously sell XYZ on another market for a higher price, the trade would result in a profit with little risk. The buying and selling pressure in the two markets will move the price difference between the markets towards equilibrium, quickly eliminating any opportunity for arbitrage.

That is, we can determine the value of a financial instrument if we assume arbitrage to be unavailable. Using this principle, we can value options under the assumption that no arbitrage opportunities exist.

When trying to understand arbitrage as it relates to stock and options markets, we often assume no restrictions on borrowing money, no restrictions on borrowing shares of stock, and no transactions costs. In the real world, such restrictions do exist and, of course, transaction costs are present which may reduce or eliminate any perceived arbitrage opportunity for most individual investors.

For investors with access to large amounts of capital, low fee structures and few restrictions on borrowing, arbitrage may be possible at times, although these opportunities are fairly rare.

Options are derivatives; they derive their value from other factors. In the case of stock options, the value is derived from the underlying stock, interest rates, dividends, anticipated volatility and time to expiration.

There are certain factors that must hold true for options under the no arbitrage principle. If the September call is less expensive, investors would buy the September call, sell the June call and guarantee a profit. Note that XYZ is a non-dividend paying stock, the options are American exercise style and interest rates are expected to be constant over the life of both options. Here is an example of why a longer term option premium must be equal to or greater than the premium of the short term option.

In our interest free, commission free, hypothetical world, the timing of the assignment does not matter, however the exercise would only occur after an assignment. If the June premium was higher like in the example , investors would sell the June call, causing the price to decline and buy the September, causing the price of that option to rise.

These trades would continue until the price of the June option was equal to or below the price of the September option. A similar relationship can be seen between two different strike prices but the same expiration. With stock and options, there are six possible positions from three securities when dividends and interest rates are equal to zero — stock, calls and puts:. Synthetic relationships with options occur by replicating a one part position, for example long stock, by taking a two part position in two other instruments.