Theta

Theta is the rate of change in an instrument's price with respect to the time to expiry.

Theta includes both of the following elements:

Time decay—the change in the instrument's value as time moves forward, that is, as the expiry date moves closer, i.e., as the time to expiration decreases. It is the ratio of the change in the price of the portfolio(s) to the decrease in time to expiration. It is calculated as the TV price tomorrow minus the TV price today.

In SD applications this calculation:

Is based on the assumption that no other market parameters (spot, volatility or interest rates) change, and that the value of an option (portfolio) tomorrow is calculated using the identical market parameters used to calculate the value of an option (portfolio) today. That is, the same volatility is used to value an option tomorrow as is used to value the option today.

Takes into account holidays and weekends. That is, if “tomorrow” falls on a holiday or weekend, “tomorrow” becomes the next business day. For example, if today is Friday and there is a holiday in the US on Monday, the theta for USD options will include four days of time decay rather than one.

Cost of carry—the interest rate sensitivity that causes the value of the portfolio to change as time progresses, e.g., the cost of carry on spots and forwards is included in the theta value.