Question

1. A call option on XYZ stock has a delta of 0.4483, and a put option on XYZ stock with same strike and date to expiration has a delta of −0.5517. The stock is currently trading for $48.00. The gamma for both the call and put is 0.07. What is the price of the call option?

Answer 1

We know that ∆c = e −δT N(d1)

∆p = −e −δT N(−d1)

Therefore ∆c − ∆p = e −δT = 1

Hence we can get δ = 0.

Since ∆c = N(d1) = 0.4483, we can get d1 = −0.126.

For the gamma, Γc = 1 Sσ√ T ( 1 √ 2π e − d 2 1 2 ) = 0.07

Therefore σ √ T = 0.1178.

d2 = d1 − σ √ T = −0.2438

and hence N(d2) = 0.4037.

Since d1 = ln( S K ) + (r − δ + 1 2 σ 2 )T σ √ T = −0.126

We can get Ke−rT = 49.057.

Therefore C = SN(d1) − Ke−rT N(d2) = 1.7957