Coupon Accepted Successfully!




  • The theta of an option is the rate of change in its value with the passage of time, assuming that other things remain the same
  • For a portfolio, the theta is the rate of change in the value of the portfolio as time passes, given that other things are constant.  A positive theta implies that the portfolio value will increase as the time passes, while a negative theta implies that the value will decrease with the passage of time, if there is little move in the stock price and the implied volatility
  • Normally expect the theta of an option to be negative as with the passage of time, an option
  • loses value
    • Exception can be an in-the money European put option on a non dividend paying stock
  • For at-the-money option, theta increases as the expiration date nears
    • Theta decreases as an option which is either out of money or in the money approaches expiration


  • We have theta of call given by:



  • Where:


  • For a put option, theta is given by:
  • Where:    
    • S0 = Stock price at time 0, i.e. present price of the stock
    • d1 and d2 are as defined in the Black-Scholes Pricing formula earlier
    • σ = Stock price volatility
    • K = Strike price
    • T = Time of maturity of the option measured in years, so that 6 months will be 0.5 years
    • r = Risk neutral rate of interest

Test Your Skills Now!
Take a Quiz now
Reviewer Name