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# What determines the cost of an option

Email Email You can't know where you are going until you know where you've been. You can't price an option until you know what makes up its value. An options trade can become a complex machine of legs, multiple orders, adjustments, and Greeks, but if you don't know the fundamentals then what are you trying to accomplish?

## Valuation of options

When you look at an option chain have you ever wondered how they generated all those prices for the options? These options are not created by random but instead calculated out using a model such as the Black-Scholes Model. We will dive deeper into the seven components of the Black-Scholes Model and how and why they are used to derive an option's price. Like all models, the Black-Scholes Model does have a weakness and is far from perfect.

### Major Factors Influencing Options Premium

It was developed by Fisher Black and Myron Scholes what determines the cost of an option a way to estimate the price of an option over time. Robert Merton later published a follow-up paper further expanding the understanding of the model. Merton is credited for naming the model "Black-Scholes. Fisher Black was not eligible because the Nobel Prize cannot be awarded posthumously. As with any model, some assumptions have to be understood. The rate of return on the riskless asset is constant The underlying follows the more the option will be worth which states that move in a random and unpredictable path There is no arbitrage, riskless profit, opportunity It is possible to borrow and lend any amount of money at the riskless rate It is possible to buy or short any amount of stock There are no fees or cost There are seven factors in the model: stock price, strike price, type of option, time to expiration, interest rates, dividends and future volatility.

### Intrinsic Value

Of the seven factors, only one is not known with any certainty: future volatility. This is the main area where the model can skew the results. Stock Price If a call option allows you to buy a stock at a specified price in the future than the higher that price goes, the more the option will be worth.

In this situation, our option value will be higher. Strike Price Strike price follows along the same lines as stock price. When we classify strikes, we do it as in-the-money, at-the-money or out-of-the-money. When a call option is in-the-money, it means the stock price is higher than the strike price. When a call is out-of-the-money, the stock price is less than the strike price. On the flip side of that coin, a put option is in-the-money when the stock price is less than the strike price.

A put option is out-of-the-money when the stock price is higher than the strike price. Options that are in-the-money have a higher value compared to options that are out-of-the-money.

### Introduction to Options Pricing

Type Of Option This is probably the easiest factor to understand. An option is either a put or a call, and the value of the option will change accordingly. A call option gives the holder the right to buy the underlying at a specified price within a specific time period.

A put option gives the holder the right to sell the underlying at a specified price within a specific time period. If you are long a call or short a put your option value increases as the market moves higher.

If you are long a put or short a call your option value increases as the market moves lower. Time To Expiration Options have a limited lifespan thus their value is affected by the passing of time. As the time to expiration increases the value of the option increases. As the time to expiration gets closer the value of the option begins to decrease. The value begins to rapidly decrease within the last thirty days of an option's life.

The more time an option has till expiration, the more time the option has to move around.

Interest Rates Interest rates have a minimal effect on an option's value. When interest rates rise a call option's value will also rise, and a put option's value will fall. Plus we will have the same reward potential for half the risk.

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Now we can take that extra cash and invest it elsewhere such as Treasury Bills. This would generate a guaranteed return on top of our investment in TOP. The higher the interest rate, the more attractive the second option becomes. Thus, when interest rates go up, calls are a better investment, so their price also increases.

On the flip side of that coin if we look at a long put versus a long call, we can see a disadvantage. We have two options when we want to play an underlying to the downside. You can short shares of the stock which would generate cash into the brokerage and allow us to earn interest on that cash. You long a put which will cost you less money overall but not put extra cash into your brokerage that generates interest income.

As a result, time value is often referred to as an option's extrinsic value since time value is the amount by which the price of an option exceeds the intrinsic value. Time value is essentially the risk premium the option seller requires to provide the option buyer the right to buy or sell the stock up to the date the option expires. Typically, stocks with high volatility have a higher probability for the option to be profitable or in-the-money by expiry. As a result, the time value—as a component of the option's premium—is typically higher to compensate for the increased chance that the stock's price could move beyond the strike price and expire in-the-money. For stocks that are not expected to move much, the option's time value will be relatively low.

The higher the interest rate, the more attractive the first option becomes. Thus, when interest rates rise the value of put options drops. Dividends Options do not receive dividends, so their value fluctuates when dividends are released. When a company releases dividends, they have an ex-dividend date. If you own the stock on that date, you will be awarded the dividend. Also on what determines the cost of an option date, the value of the stock will decrease by the amount of dividend.

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As dividends web leader online earnings a put option's value also increases and a calls' value decreases. Volatility Volatility is the only estimated factor in this model.

## Options Pricing

The volatility that is used is forward volatility. Forward volatility is the measure of implied volatility over a period in the future. Implied volatility shows the "implied" movement in a stock's future volatility.

The Bottom Line Options are contracts that give option buyers the right to buy or sell a security at a predetermined price on or before a specified day. The price of an option, called the premiumis composed of a number of variables. Options traders need to be aware of these variables so they can make an informed decision about when to trade an option. When investors buy options, the biggest driver of outcomes is the price movement of the underlying security or stock.

It tells you how traders think the stock will move. Implied volatility is always expressed as a percentage, non-directional and on an annual basis.

## What Is the Value of a Call or Put Option?

The higher the implied volatility, the more people think the stock's price will move. Stocks listed on the Dow Jones are value stocks, so a lot of movement is not expected.

Thus, they have lower implied volatility. Growth stocks or small caps found on the Russellconversely, are expected to move around a lot, so they carry higher implied volatility. Conclusion The Black-Scholes Model is used to derive an option's value.

While there are many assumptions in the equation, the Black-Scholes Model is still the most widely used model. Its ease of calculation and useful approximation create a strong basis to build more complex models. Out of the seven factors volatility is the only one that is estimated. Out of the seven factors, the most important are stock price, strike price, type of option, time to expiration and volatility. Interest rates and dividends have a very minuscule effect on an option's value.

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