Question

Q5. Gamma vs. theta

You short an ATM straddle, ie 1x ATM CALL + 1x ATM PUT.

Q5a. What is the gamma and delta value of the position?

Q5b. How much theta are you paying or collecting each day?

Q5c. Underlying moved down by $5 in a single day. How much should the price move based on

i. delta; ii gamma; iii. theta

Answer 1

Short Straddles involve selling a Call and a Put option at the same strike price . Given that Short straddle is at the Money , please find the answers below :

5 A) Delta measures the speed at which the option price moves with respect to change in price of underlying asset.

Since the straddle is at the money , the strike price will be equal to the current spot price , Delta should be zero.

Gamma is the rate of change in delta for a single unit movement in price of underlying asset.

At the strike price , Gamma will have the lowest value possible and it will be negative

5 B) Thetha is the rate of decline in the price of an option due to passage of time.

For a short straddle trader , the best return would be when the straddle is at the money i.e.,Strike price = Spot Price. Hence , the thetha would be highest in this case since the straddle is at the money.

5 C) The underlying asset moved down by 5 dollars in a single day.

1) Based on Delta , the price movement will not be significant because delta is close to zero at the strike price . Hence , the price movement will be very less or close to zero.

2) Based on Gamma , the price of the option will rise because the short put rises in price more than the fall in price of call . This can also be explained by negative gamma .

3) When underlying asset price comes down , the sensitivity of change in option price due to time expiration will also fall and the short straddle price falls.