Options Premium

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In finance, a put or put option is a stock market device which gives the owner of a put the right, but not the obligation, to sell an asset the underlyingat a specified price the strikeby a predetermined date the expiry or maturity to a given party the seller of the put.

The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying. Put options are most commonly used in option premium to stock price ratio stock market to protect against the decline of the price of a stock below a specified price. In this way the buyer of the put will receive at least the strike price specified, even if the asset is currently worthless.

If the strike is Kand at time t the value of the underlying is S tthen in an American option the buyer can exercise the put for a payout of K-S t any time until the option's maturity time T. The put yields a positive return only if the security price falls below the strike when the option is exercised.

A European option can only be option premium to stock price ratio at time T rather than any option premium to stock price ratio until Tand a Bermudan option can be exercised only on specific dates listed in the terms of the contract. If the option is not exercised by maturity, it expires worthless. The buyer will not exercise the option at an allowable date if the price of the underlying is greater than K. The most obvious use of a put is as a type of insurance. In the protective put strategy, the investor buys enough puts to cover his holdings of the underlying so that if a drastic downward movement of the underlying's price occurs, he has the option to sell the holdings at the strike price.

Another use is for speculation: Puts may also be combined with other derivatives as part of more complex investment strategies, and in particular, may be useful for hedging.

By put-call paritya European put can be replaced by buying the appropriate call option and selling an appropriate forward contract. The terms for exercising the option's right to sell it differ depending on option style.

A European put option allows the holder to exercise the put option for a short period of time right before expiration, while an American put option allows exercise at any time before expiration. The put buyer either believes that the underlying asset's price will fall by the exercise date or hopes to option premium to stock price ratio a long position in it.

The advantage of option premium to stock price ratio a put over short selling the asset is that the option owner's risk of loss is limited to the premium paid for it, whereas the asset short seller's risk of loss is unlimited its price can rise greatly, in fact, in theory it can rise infinitely, and such a rise is the short seller's loss.

The put option premium to stock price ratio believes that the underlying security's price will rise, not fall. The writer sells the put to collect the premium. The put writer's total potential loss is limited to the put's strike price less the spot and premium already received. Puts can be used also to limit the writer's portfolio risk and may be part of an option spread.

That is, the buyer wants the value of the put option to increase by a decline in the price of the underlying asset below the strike price. Option premium to stock price ratio writer seller of a put is long on the underlying asset and short on the put option itself. That is, the seller wants the option to become worthless by an increase in the price of the underlying asset above the strike price.

Generally, a put option that is purchased is referred to as a long put and a put option that is sold is referred to as a short put. A naked putalso called an uncovered putis a put option whose writer the seller does not have a position in the underlying stock or other instrument.

This strategy is best used by investors who want to accumulate a position in the underlying stock, but only if the price is low enough. If the buyer fails to exercise the options, then the writer keeps the option premium as a "gift" for playing the game. If the underlying stock's market price is below the option's strike price when expiration arrives, the option owner buyer can exercise the put option, forcing the writer to buy the underlying stock at the strike price.

That allows the exerciser buyer to profit from the difference between the stock's market price and the option's strike price. But if the stock's market price is above the option's strike price at the end of expiration day, the option expires worthless, and the owner's loss is limited to the premium fee paid for it the writer's profit.

The seller's potential loss on a naked put can be substantial. If the stock falls all the way to zero bankruptcyhis loss is equal to the strike price at option premium to stock price ratio he must buy the stock to cover the option minus the premium received.

The potential upside is the premium received when selling the option: During the option's lifetime, if the stock moves lower, the option's premium may increase depending on how far the stock falls and how much time passes. If it does, it becomes more costly to close the position repurchase the put, sold earlierresulting in a loss. If the stock price completely collapses before the put position is closed, the put writer potentially can face catastrophic loss.

In order to protect the put buyer from default, the put writer is required to post margin. The put buyer does not need to post margin because the buyer would not exercise the option if it had a negative payoff.

A buyer thinks the price of a stock will decrease. He pays a premium which he will never get back, unless it is sold before it expires. The buyer has the right to sell the stock at the strike price.

The writer receives a premium from option premium to stock price ratio buyer. If the buyer exercises his option, the writer will buy the stock at the strike price. If the buyer does not exercise his option, the writer's profit is the premium. A put option is said to have intrinsic value when option premium to stock price ratio underlying instrument has a spot price S below the option's strike price K. Upon exercise, a put option is valued at K-S if it is " in-the-money ", otherwise its value is zero.

Prior to exercise, an option has time value apart from its intrinsic value. The following factors reduce the time value of a put option: Option pricing is a central problem of financial mathematics. Trading options involves a constant monitoring of the option value, which is affected by changes in the base asset price, volatility and time decay. Moreover, the dependence of the put option value to those factors is not linear — which makes the analysis even more complex.

The graphs clearly shows the non-linear dependence of the option value to the base asset price. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.

November Learn how and when to remove this template message. Energy derivative Freight derivative Inflation derivative Property derivative Weather derivative. Retrieved from " https: Articles needing additional references from November All articles needing additional references. Views Read Edit View history. This page was last edited on 18 Januaryoption premium to stock price ratio By using this site, you agree to the Terms of Use and Privacy Policy.

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Commodity option pricing formula

Because the price of options depends on the price of the underlying asset and because options are a wasting asset due to their limited lifetimes, option premiums vary with the price and volatility of the underlying asset and time to expiration of the options contract.

Several ratios have been developed to measure this change in price with respect to the price or volatility of the underlying, and the effect of time decay. Since most of these ratios are represented by Greek letters—delta, gamma, theta, and rho—the group is often referred to simply as the greeks. Vega is also a commonly used ratio and is also considered a greek, although it is not actually a Greek letter some purists prefer to use the Greek letter tau for vega.

These ratios are used to measure potential changes in the value of an actual portfolio or of test portfolios of options from potential changes in the underlying stock price, volatility, or time until expiration. The delta ratio is the percentage change in the option premium for each dollar change in the underlying. Note that a put option with the same strike price will decline in price by almost the same amount, and will therefore have a negative delta.

Options are frequently used to hedge risk. But what if earnings are less than what the market expected. Then the price may drop a few dollars, resulting in a loss. Therefore, you would want to buy 2 put contracts to cover or hedge your position. Since the value of the portfolio doesn't change within a narrow range, it is said to be delta neutral. This technique is also called delta hedging.

The delta of a portfolio, which is calculated by summing the deltas of each option in the portfolio, is sometimes called its position delta. Delta is also used as a proxy for the probability that a call will expire in the money.

However, delta does not measure probability per se. Delta can serve as a proxy for the probability only because both delta and the probability that a call will go or stay in the money increases as the option goes further into the money.

However, delta is not a direct measure of the probability. As an example of where delta and probability will diverge is on the last trading day of the option.

Most of the value of a call will depend on the intrinsic value, which is the amount that the underlying price exceeds the strike price of the call. The above example will not work out perfectly in the real world. You may even ask, why adopt a delta neutral portfolio when your objective is to make a profit?

A delta neutral portfolio is only delta neutral within a narrow price range of the underlying. Delta itself changes as the price of the underlying changes. Then you would profit from the puts, but lose on the stock. So would the profit from the puts completely neutralize the loss on the stock.

Actually, you would do better. This results because delta itself changed. Gamma is the change in delta for each unit change in the price of the underlying. The absolute magnitude of delta increases as the time to expiration of the option decreases, and as its intrinsic value increases.

Gamma changes in predictable ways. As an option goes more into the money, delta will increase until it tracks the underlying dollar for dollar; however, delta can never be greater than 1 or less than When delta is close to 1 or -1, then gamma is near zero, because delta doesn't change much with the price of the underlying. Gamma and delta are greatest when an option is at the money—when the strike price is equal to the price of the underlying.

The change in delta is greatest for options at the money, and decreases as the option goes more into the money or out of the money. Both gamma and delta tend to zero as the option moves further out of the money. The total gamma of a portfolio is called the position gamma. Options are a wasting asset.

The option premium consists of a time value that continuously declines as time to expiration nears, with most of the decline occurring near expiration. Theta is a measure of this time decay, and is expressed as the loss of time value per day.

Thus, a theta of -. Theta is minimal for a long-term option because the time value decays only slowly, but increases as expiration nears, since each day represents a greater percentage of the remaining time. Theta is also greatest when the option is at the money, because this is the price where the time value is greatest, and, thus, has a greater potential to decay.

For the same reason, theta is greater for more volatile assets, because volatility increases the option premium by increasing the time value of the premium.

With higher volatility, an option has a greater probability of going into the money for any given unit of time. For the option writer, theta is positive, because options are more likely to expire worthless with less time until expiration. Theta measures changes in value of options or a portfolio that is due to the passage of time. The holding of options has a negative position theta because the value of options continuously declines with time. Because time decay favors the option writer, a short position in options is said to have positive position theta.

The net of the positive and negative position thetas is the total position theta of the portfolio. Volatility is the variability in the price of the underlying over a given unit of time. The Black-Scholes equation includes volatility as a variable because it affects the probability of the option going into the money: Historical volatility is easily measured, but current volatility cannot be measured because the unit of time is reduced to now. On the other hand, the price of the underlying, the option premium, time until expiration, and the other factors, except volatility, are known.

Therefore, volatility can be measured by rearranging the Black-Scholes equation to solve for volatility in terms of the other known factors. This is referred to as implied volatility , because the volatility is implied by the other known variables to the Black-Scholes equation. Consequently, vega is often used to measure the change in implied volatility.

Vega measures the change in the option premium due to changes in the volatility of the underlying, and is always expressed as a positive number. Because volatility only affects time value, vega tends to vary like the time value of an option—greatest when the option is at the money and least when the option is far out of the money or in the money.

The position vega measures the change in option or portfolio values with changes in the volatility of the underlying. Higher interest rates generally result in higher call premiums, according to option pricing models , because the present value of the strike price is subtracted in these models. Hence, higher interest rates correspond to lower present values, so less is subtracted, leading to higher call prices. A more intuitive way to understand why higher interest rates increases call prices is to understand that a call is like a forward contract, in that it allows the holder to buy the stock at a specified price before the expiration date, so the money that would have been used to otherwise buy the stock can, instead, be invested in Treasuries to earn a risk-free interest rate until the date in which the stock is purchased.

Because the stockholder incurs a cost of holding the stock, which is the forfeited interest that could otherwise be earned, a higher price is charged for the call to compensate the stockholder for the forfeited interest.

By the same reasoning, dividends decrease the price of calls because only the stockholder is entitled to receive the dividends, not the call holder. On the other hand, the application of the put-call parity theorem to option pricing models yields lower put premiums due to higher interest rates.

Thus, a rho of 0. The values are theoretical because it is market supply and demand that ultimately determines prices. In fact, rho can be misleading because interest rates may have a larger effect on the price of the underlying, which is a more significant determinant of option prices.

The demand for stocks, for instance, varies inversely with interest rates. When interest rates are low, investors buy stocks in an attempt to earn more income. When interest rates rise, risk-averse investors move their money from stocks to safer bonds and other interest-paying investments. Thus, puts will tend to increase with interest rates while calls will decrease, because the price of the underlying will have a more significant effect on option premiums than the interest rate.