Assume that a $50 strike call has a 3.0% continuous dividend,σ = 0.27,r = 0.06 and 60 days from expiration.What is the gamma for a stock price movement from $48.00 to $49.00?

Question

Quizplus · Accepted Answer

To calculate the gamma, we need to first calculate the d1 and d2 values using the Black-Scholes model:

d1 = [ln(S/K) + (r - q + 0.5σ²)t]/(σ√t) = [ln(48/50) + (0.06 - 0.03 + 0.5(0.27)²(60/365))]/(0.27√(60/365)) = -0.2775
d2 = d1 - σ√t = -0.4879

Next, we can use the gamma formula:

Gamma = e^(-qT) * N'(d1) / (Sσ√T) = e^(-0.03*(60/365)) * N'(-0.2775) / (48*0.27√(60/365)) = 0.074

Therefore, the gamma for a stock price movement from $48.00 to $49.00 is 0.074, which is closest to option B.

Assume That a $50 Strike Call Has a 3