Understanding Option Theta in Excel

Option’s Rho is a measure of how sensitive an option’s price is to changes in the risk-free interest rate. The risk-free interest rate is the theoretical rate of return on a riskless investment, such as a U.S. Treasury bill. Option’s Rho indicates how much the option’s price will change for a one-percentage-point change in the risk-free interest rate.

For example, if an option has a Rho of 0.5, it means that for every 1% increase in the risk-free interest rate, the option’s price will increase by 0.5%. Conversely, for every 1% decrease in the risk-free interest rate, the option’s price will decrease by 0.5%. Option’s Rho can be positive or negative, depending on whether the option is a call or a put.

Call options are contracts that give the buyer the right to buy an underlying asset at a specified price before or on a certain date. Put options are contracts that give the buyer the right to sell an underlying asset at a specified price before or on a certain date.

Generally speaking, call options have positive Rho and put options have negative Rho. This is because call options benefit from higher interest rates and put options suffer from higher interest rates. Higher interest rates make it more attractive to buy an asset than to sell it, so call options increase in value when interest rates rise and decrease in value when interest rates fall.

However, there are some exceptions to this rule. For example, some long-term call options may have negative Rho if they are based on assets that have negative real returns when interest rates rise. Similarly, some short-term put options may have positive Rho if they are based on assets that have positive real returns when interest rates fall.

Option’s Rho can also vary depending on other factors, such as the strike price of the option, the time to expiration of the option, and the volatility of the underlying asset. Generally speaking, longer-term options have higher Rho than shorter-term options because they are more sensitive to changes in future cash flows and expectations.

Basic Theory of Option Theta:

Theta is an essential Greek in options trading, representing the time decay of an option’s premium. As time passes, the value of an option decreases, and Theta quantifies this decay. It is crucial for option traders to understand how time impacts the value of their positions.

The formula for Theta (θ) is typically expressed as follows:

Where:

• is the option’s Theta,
• is the option’s value, and
• is time.

Procedures for Calculating Option Theta in Excel:

To calculate Theta in Excel, you can use the built-in function called “NORMSDIST” for normal distribution. The formula for Theta is derived from the Black-Scholes model:

Where:

• is the current stock price,
• is the standard normal distribution,
• is the volatility of the stock, and
• is the time to expiration.

Scenario and Example:

Let’s consider a scenario where you have a call option with the following parameters:

• Stock Price (): $100
• Strike Price (): $105
• Time to Expiration (): 30 days
• Volatility (): 0.2 (20%)
• Risk-Free Rate (): 0.05 (5%)

Using the Black-Scholes formula, we can calculate the option price and Theta.

can be obtained using Excel’s NORMSDIST function.

Now, let’s create an Excel table with these values and calculate Theta:

Parameter	Value
Stock Price (S)	$100
Strike Price (K)	$105
Time to Expiration (T)	30 days
Volatility ()	20%
Risk-Free Rate (r)	5%

Excel Formulas:

Result: