# Stock Option

You do not need to know all the academic stuff like all five greeks and and other fancy mathematical models. Suggest a new Definition Proposed definitions will be considered for inclusion in the Economictimes. You suspect that the price of the eggs is going to increase because of the cold weather. Yes, indeed, it ended last year. Writers can protect themselves by writing covered calls.

The option holder has the benefit of purchasing the stock at a discount from its current market value if the stock price increases prior to expiration. For example, if the strike price of an option is $10, the trader buys the option for $, and the underlying stock increases to $12 at expiration, the traders nets $ per share, while only having put .

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If the buyer is right, and the stock rises above the strike price, the buyer will be able to acquire the stock for a lower price strike price and then sell it for a profit at the current market price. Risk to the call buyer is limited to the premium paid for the option, no matter how much the underlying stock moves.

The profit at expiration, if applicable, is: This will give the total profit or loss to the trader in dollars. The risk to the call writer is much greater. Their maximum profit is the premium received, but they face infinite risk because the stock price could continue to rise against them.

To offset this risk, many option writers use covered calls. The opposite is true for a put option writer. For example, a put option buyer is bearish on the underlying stock and believes its market price will fall below the specified strike price on or before a specified date.

If the underlying stock's price closes above the specified strike price on the expiration date, the put option writer's maximum profit is achieved.

They get to keep the entire premium received. Conversely, a put option holder benefits from a fall in the underlying stock's price below the strike price. If the underlying stock's price falls below the strike price, the put option writer is obligated to purchase shares of the underlying stock at the strike price.

This is then multiplied by if each contract is shares and the number of contracts bought. The risk to the option writer if the stock price falls is that they have to buy the stock at the strike price.

Some traders write put options at strike prices where they want to buy stock anyway. They get the stock at the price they want, with the added benefit of receiving the option premium.

A put options gives the owner the right to sell a specified amount Learn the top three risks and how they can affect you on either side of an options trade. The trader selling a call has an obligation to sell the stock to the call buyer at a fixed price "strike price".

If the seller does not own the stock when the option is exercised, he is obligated to purchase the stock from the market at the then market price. If the stock price decreases, the seller of the call call writer will make a profit in the amount of the premium. If the stock price increases over the strike price by more than the amount of the premium, the seller will lose money, with the potential loss being unlimited.

A trader who expects a stock's price to increase can buy the stock or instead sell, or "write", a put. The trader selling a put has an obligation to buy the stock from the put buyer at a fixed price "strike price".

If the stock price at expiration is above the strike price, the seller of the put put writer will make a profit in the amount of the premium.

If the stock price at expiration is below the strike price by more than the amount of the premium, the trader will lose money, with the potential loss being up to the strike price minus the premium. Combining any of the four basic kinds of option trades possibly with different exercise prices and maturities and the two basic kinds of stock trades long and short allows a variety of options strategies.

Simple strategies usually combine only a few trades, while more complicated strategies can combine several. Strategies are often used to engineer a particular risk profile to movements in the underlying security. For example, buying a butterfly spread long one X1 call, short two X2 calls, and long one X3 call allows a trader to profit if the stock price on the expiration date is near the middle exercise price, X2, and does not expose the trader to a large loss.

Selling a straddle selling both a put and a call at the same exercise price would give a trader a greater profit than a butterfly if the final stock price is near the exercise price, but might result in a large loss. Similar to the straddle is the strangle which is also constructed by a call and a put, but whose strikes are different, reducing the net debit of the trade, but also reducing the risk of loss in the trade.

One well-known strategy is the covered call , in which a trader buys a stock or holds a previously-purchased long stock position , and sells a call. If the stock price rises above the exercise price, the call will be exercised and the trader will get a fixed profit.

If the stock price falls, the call will not be exercised, and any loss incurred to the trader will be partially offset by the premium received from selling the call. Overall, the payoffs match the payoffs from selling a put. This relationship is known as put-call parity and offers insights for financial theory. Another very common strategy is the protective put , in which a trader buys a stock or holds a previously-purchased long stock position , and buys a put.

This strategy acts as an insurance when investing on the underlying stock, hedging the investor's potential loses, but also shrinking an otherwise larger profit, if just purchasing the stock without the put. The maximum profit of a protective put is theoretically unlimited as the strategy involves being long on the underlying stock. The maximum loss is limited to the purchase price of the underlying stock less the strike price of the put option and the premium paid. A protective put is also known as a married put.

Another important class of options, particularly in the U. Other types of options exist in many financial contracts, for example real estate options are often used to assemble large parcels of land, and prepayment options are usually included in mortgage loans. However, many of the valuation and risk management principles apply across all financial options.

There are two more types of options; covered and naked. Options valuation is a topic of ongoing research in academic and practical finance. In basic terms, the value of an option is commonly decomposed into two parts:.

Although options valuation has been studied at least since the nineteenth century, the contemporary approach is based on the Black—Scholes model which was first published in The value of an option can be estimated using a variety of quantitative techniques based on the concept of risk neutral pricing and using stochastic calculus.

The most basic model is the Black—Scholes model. More sophisticated models are used to model the volatility smile. These models are implemented using a variety of numerical techniques. More advanced models can require additional factors, such as an estimate of how volatility changes over time and for various underlying price levels, or the dynamics of stochastic interest rates.

The following are some of the principal valuation techniques used in practice to evaluate option contracts. Following early work by Louis Bachelier and later work by Robert C. Merton , Fischer Black and Myron Scholes made a major breakthrough by deriving a differential equation that must be satisfied by the price of any derivative dependent on a non-dividend-paying stock.

By employing the technique of constructing a risk neutral portfolio that replicates the returns of holding an option, Black and Scholes produced a closed-form solution for a European option's theoretical price. While the ideas behind the Black—Scholes model were ground-breaking and eventually led to Scholes and Merton receiving the Swedish Central Bank 's associated Prize for Achievement in Economics a.

Nevertheless, the Black—Scholes model is still one of the most important methods and foundations for the existing financial market in which the result is within the reasonable range. Since the market crash of , it has been observed that market implied volatility for options of lower strike prices are typically higher than for higher strike prices, suggesting that volatility is stochastic, varying both for time and for the price level of the underlying security.

Stochastic volatility models have been developed including one developed by S. Once a valuation model has been chosen, there are a number of different techniques used to take the mathematical models to implement the models. In some cases, one can take the mathematical model and using analytical methods develop closed form solutions such as Black—Scholes and the Black model.

The resulting solutions are readily computable, as are their "Greeks". Although the Roll-Geske-Whaley model applies to an American call with one dividend, for other cases of American options , closed form solutions are not available; approximations here include Barone-Adesi and Whaley , Bjerksund and Stensland and others.

Closely following the derivation of Black and Scholes, John Cox , Stephen Ross and Mark Rubinstein developed the original version of the binomial options pricing model.

The model starts with a binomial tree of discrete future possible underlying stock prices. By constructing a riskless portfolio of an option and stock as in the Black—Scholes model a simple formula can be used to find the option price at each node in the tree.

This value can approximate the theoretical value produced by Black Scholes, to the desired degree of precision. However, the binomial model is considered more accurate than Black—Scholes because it is more flexible; e. Binomial models are widely used by professional option traders. The Trinomial tree is a similar model, allowing for an up, down or stable path; although considered more accurate, particularly when fewer time-steps are modelled, it is less commonly used as its implementation is more complex.

For a more general discussion, as well as for application to commodities, interest rates and hybrid instruments, see Lattice model finance. For many classes of options, traditional valuation techniques are intractable because of the complexity of the instrument.

In these cases, a Monte Carlo approach may often be useful. Rather than attempt to solve the differential equations of motion that describe the option's value in relation to the underlying security's price, a Monte Carlo model uses simulation to generate random price paths of the underlying asset, each of which results in a payoff for the option.

The average of these payoffs can be discounted to yield an expectation value for the option. The equations used to model the option are often expressed as partial differential equations see for example Black—Scholes equation. Once expressed in this form, a finite difference model can be derived, and the valuation obtained. A number of implementations of finite difference methods exist for option valuation, including: A trinomial tree option pricing model can be shown to be a simplified application of the explicit finite difference method.

Other numerical implementations which have been used to value options include finite element methods. Additionally, various short rate models have been developed for the valuation of interest rate derivatives , bond options and swaptions.

These, similarly, allow for closed-form, lattice-based, and simulation-based modelling, with corresponding advantages and considerations. As with all securities, trading options entails the risk of the option's value changing over time.

However, unlike traditional securities, the return from holding an option varies non-linearly with the value of the underlying and other factors. Therefore, the risks associated with holding options are more complicated to understand and predict. This technique can be used effectively to understand and manage the risks associated with standard options. We can calculate the estimated value of the call option by applying the hedge parameters to the new model inputs as:.

A special situation called pin risk can arise when the underlying closes at or very close to the option's strike value on the last day the option is traded prior to expiration. The option writer seller may not know with certainty whether or not the option will actually be exercised or be allowed to expire. Therefore, the option writer may end up with a large, unwanted residual position in the underlying when the markets open on the next trading day after expiration, regardless of his or her best efforts to avoid such a residual.

A further, often ignored, risk in derivatives such as options is counterparty risk. In an option contract this risk is that the seller won't sell or buy the underlying asset as agreed. The risk can be minimized by using a financially strong intermediary able to make good on the trade, but in a major panic or crash the number of defaults can overwhelm even the strongest intermediaries.

From Wikipedia, the free encyclopedia. For the employee incentive, see Employee stock option. Derivatives Credit derivative Futures exchange Hybrid security.

Foreign exchange Currency Exchange rate. Binomial options pricing model. Monte Carlo methods for option pricing. Finite difference methods for option pricing.

## What It Is

Call options provide the option buyer with the right to buy an underlying security at the strike price, so the buyer wants the stock to go up. Conversely, the option writer needs to give the underlying security to the option buyer, at the strike price, in the event that the stock's market price exceeds the strike price. The owner of an option may on-sell the option to a third party in a secondary market, in either an over-the-counter transaction or on an options exchange, depending on the option. The market price of an American-style option normally closely follows that of the underlying stock, being the difference between the market price of the stock and the . Stock options contracts are for shares of the underlying stock - an exception would be when there are adjustments for stock splits or mergers. Options are traded on securities marketplaces among institutional investors, individual investors, and professional traders and trades can be for one contract or for many.