# Formulas for calculating options

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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.

During his two-decade career in Asia and the US, Nathan has consulted in strategy, valuations, corporate finance and financial planning. Options, which come in the form of calls and puts, grant a right, but not an obligation to a buyer.

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.

We provide simple formulas for pricing both the European and American options. In response to these limitations, Duffie et alEraker et al and Eraker introduced discontinuous stochastic volatility models. However, this increases the number of the parameters to be estimated. Eberlein and Keller and Eberlein et al used inverse Gaussian distribution. Carr and Wu introduced an asymmetric stable distribution model.

One of the metrics used to measure volatile stocks is called beta. Beta measures the volatility of a stock when compared to the overall market.

Volatile stocks tend to have high betas primarily due to the uncertainty of the price of the stock before the option expires. However, high beta stocks also carry more risk than low-beta stocks.

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In other words, volatility is a double-edged sword, meaning it allows investors the potential for significant returns, but volatility can also lead to significant losses. The effect of volatility is mostly subjective and difficult to quantify.

When investors look at volatility in the past, it is called either historical volatility or statistical volatility.

Historical volatility looks back in time to show how volatile the market has been. Implied volatility measures what options traders expect future volatility will be.

As such, implied volatility is an indicator of the current sentiment of the market. It shows the trading price of GE, several strike prices, and the intrinsic and time values for the call and put options. At the time of this writing, General Electric was considered a stock with low volatility and had a beta of 0. The table below contains the pricing for formulas for calculating options calls and puts that are expiring in one month top section of the table.

The bottom section contains the prices for the GE options that expire in nine months.

Amazon is a much more volatile stock with a beta of 3. Let's compare the GE 35 call option with nine months to expiration with the AMZN 40 call option with nine months to expiration.