# Theta Of Options

Theta is the rate of change of the option price relative to the change left in time to expiration of the option. Another way of understanding theta is that it is a measure of how time decay actually affects the option premium. Hence, theta is usually negative for long options. This is because the option premium is eroded by  time decay. Overtime, in the absence of favorable price moves, the option premium will decrease.

### Illustration of theta and time decay

A buyer decides to buy an OTM call option from an option seller that has a value of \$2 from a seller. If the price of the underlying security is stagnant, the following table will illustrate how time decay helps a seller profit at the expense of the buyer of the option.

 Day Option premium Buyer’s loss Seller’s profit 0 \$1.20 0 0 1 \$1 (-\$0.20) +\$0.20 2 \$0.90 (-\$0.30) +\$0.30 …. 15 0 (-\$1.20) +\$1.20

### [Note that time decay is not linear.]

So over time, due to time decay and a stagnant price in the underlying, the buyer loses the entire premium while the seller gets to keep the entire premium of \$1.20. We say that the seller of the option has profited from time decay. In the example above, the theta to the option buyer is negative . On the other hand, the theta to the option seller is positive as the option seller gains from the erosion in time value.

### Summary

• To a net short options trade, the theta is positive. As time value erodes, the option premium decreases as well. If the short positions are closed, the trader stands to make a profit.
• To a net long options trade, the theta is negative.As time value erodes, the trader will potentially make a loss on the trade.

Gamma

Rho