Question

Let S = $100, K = $120, σ = 30%, r = 0.08, and δ = 0. a. Compute the Black-Scholes call price for 1 year to maturity and for 10 years to maturity. What happens to the option price? b. Set δ = 0.001. Repeat (a). Now what happens to the option price? What accounts for the difference?

Answer 1

Answer: a. The black-scholes call price for 1 year is 0.

For 10 years it is also 0.

Option price did not change.

b. When δ is 0.001, the black-scholes call price for 1 year is 450.012.

For 10 years it is 450.0012.

The option price changed from 450.012 to 450.0012.

The difference was due to the change of δ value from 0 to 0.001.

Explanation: using the black-scholes equation below option price is callculated based on the given values.

δk/δt+1/2σsquare×Ssquare×δsquare×k/δS+rS×δk/δS-rk=0

By calculations the options prices were obtained for the first value of δ=0 both for 1 year and 10 years and compared with when the value of δ was changed to 0.001

A change in option price was also observed as the δ values changed this lead to the difference observed.