Question

according to the black scholes merton model, if a call option has a delta of 0.8, then what is the delta of the put option written on the same underlying asset with the same strike and maturity?

1. 0.8

2.. 0.2

3. -0.8

4. -0.2

Answer 1

Delta is a measure of sensitivity of an option's price with respect to the price of underlying asset. The call option delta ranges from 0 to 1 and put option delta ranges from -1 to 0. When the price of underlying increases, the price of put will fall. Delta has additive property and delta of a long stock position is +1.

It is known that ,

A long call + short put = long stock

Thus, delta of long call - delta of long put = delta of long stock. ( the delta of short put is equal to negative delta of long put)

0.80 - delta of long put = +1

Thus, delta of long put = -0.20.

Another method is as under:

The sum of absolute values of call option delta and put option delta is always 1.

Thus, call option delta + absolute value of put option delta = 1

Or, 0.80 + absolute value of put option delta = 1

Or, absolute value of put option delta = 0.20

But, put option's delta is negative always. So, Put option's delta = -0.20

The correct option is D. -0.20.