# Theta of call option. Formula for the calculation of the theta of a call option. Theta measures the option value's sensitivity to the passage of time.

## Theta of call option. Here is an example of how Theta tends to behave over time. A constant 40% implied volatility is being used on a 50 strike call option with XYZ equal to \$ This example, which was derived using OIC pricing calculators, assumes an interest rate of 2% and no changes to implied volatility or the underlying price during the.

We use the framework presented in the research paper to look at Theta for European Call options from a slightly different perspective. The following graph shows the value of the option at varying times to maturity. Each line represents the value overtime for a different underlying asset value S. It is calculated as the difference between the value of the option at inception and its value at expiry:. The rate at which this time premium dissipates for different values of S is given in the following graph which plots option thetas on the y-axis against the underlying asset value on the x-axis:.

The graph shows the sensitivity of theta for the option to various spot prices. For deep out of the money options there is no dissipation in the time premium. As the underlying asset value approaches the strike price the rate of dissipation increases. When the option is in the money, the rate of decay falls and then levels out for deep in the money options.

As S approaches positive infinity, i. As S approaches 0, i. The maximum rate of dissipation is reached around the point where the option is at- the-money, more specifically when the spot price is slightly greater than the strike price, i. As volatility increases the value of the option increases:.

It is not a monotonic i. As already seen above the option value declines as the option approaches maturity however depending on the money-ness of the option the theta many be increasing or a decreasing function of time:.

For at the money options the rate of decay is much higher increasing as the option approaches maturity. Consider the following at the money European Call option on a non dividend paying stock: Call option theta is calculated as follows: Theta relative to underlying asset value, S The following graph shows the value of the option at varying times to maturity.

In general as the option approaches maturity the value of the option declines. It is calculated as the difference between the value of the option at inception and its value at expiry: The rate at which this time premium dissipates for different values of S is given in the following graph which plots option thetas on the y-axis against the underlying asset value on the x-axis: As volatility increases the value of the option increases: While the option value declines overtime regardless of the level of volatility: Theta relative to time to maturity As already seen above the option value declines as the option approaches maturity however depending on the money-ness of the option the theta many be increasing or a decreasing function of time: A closer look at Black—Scholes option thetas — Douglas R.

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