Cyril is purchasing a down-and-in cash call.H = $45.00,S = $38.24,K = $35,σ = 0.33,r = 0.05,div = 0 and it expires in 140 days.What is the value of the option if the payment is $1.00?

Question

Quizplus · Accepted Answer

Using the Black-Scholes model, we can calculate the value of the down-and-in cash call option:

d1 = (ln(H/K) + (r - div + 0.5*σ^2)t) / (σ*sqrt(t)) 
d2 = d1 - σ*sqrt(t) 
d3 = (ln(H/S) + (r - div + 0.5*σ^2)t) / (σ*sqrt(t)) 
d4 = d3 - σ*sqrt(t)

N(x) is the cumulative distribution function of the standard normal distribution
N(-x) is 1 - N(x)

Option value = H*N(d1) - K*exp(-r*t)*N(d2) - S*N(d3) + K*exp(-r*t)*N(d4)

Plugging in the given values: 
t = 140/365 
d1 = 0.4447 
d2 = -0.0749 
d3 = -1.5103 
d4 = -1.1675

Option value = $0.80

Therefore, the best choice is A, as the option value is $0.80 and the payment is $1.00, resulting in a loss of $0.20.

Cyril Is Purchasing a Down-And-In Cash Call