the value of having the option of waiting longer before deciding to exercise. Even a deeply out of the money put will be worth something, as there is some chance the stock price will fall below the strike before the expiry date. However, as time approaches maturity, there is less chance of this happening, so the time value of an option is decreasing with time. Thus if you are long an option you are short theta: your portfolio will lose value with the passage of time (all other factors held constant). Rho Rho, , measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk-free interest rate (for the relevant outstanding term). Except under extreme circumstances, the value of an option is less sensitive to changes in the risk-free interest rate than to changes in other parameters. For this reason, rho is the least used of the first-order Greeks. Rho is typically expressed as the amount of money, per share of the underlying, that the value of the option will gain or lose as the risk-free interest rate rises or falls by 1.0% per annum (100 basis points). Lambda Lambda, , omega, , or elasticity is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing. It holds that . Epsilon Epsilon, (also known as psi, ), is the percentage change in option value per percentage change in the underlying dividend yield, a measure of the dividend risk. The dividend yield impact is in practice determined using a 10% increase in those yields. Obviously, this sensitivity can only be applied to derivative instruments of equity products. Second-order Greeks Gamma Gamma, , measures the rate of change in the delta with respect to changes in the underlying price. Gamma is the second derivative of the value function with respect to the underlying price. Most long options have positive gamma and most short options have negative gamma. Long options have a positive relationship with gamma because as price increases, Gamma increases as well, causing Delta to approach 1 from 0 (long call option) and 0 from −1 (long put option). The inverse is true for short options. Gamma is greatest approximately at-the-money (ATM) and diminishes the further out you go either in-the-money (ITM) or out-of-the-money (OTM). Gamma is important because it corrects for the