Assume that a $50 strike call pays a 2.0% continuous dividend,r = 0.07,σ = 0.25,and the stock price is $48.00.What is the profit or loss,per share,for a short call position if the option expires in 60 days and the price rises to $50.00 after 5 days?
A) $0.84 gain
B) $0.84 loss
C) $0.95 gain
D) $0.95 loss

Question

Quizplus · Accepted Answer

To calculate the profit or loss for a short call position, we need to first calculate the price of the call option using the Black-Scholes formula:

C = S*e^(-qT)*N(d1) - Ke^(-rT)*N(d2)

where 
S = 48, the current stock price 
q = 2.0%, the continuous dividend yield 
r = 7%, the risk-free interest rate 
T = 60/365 = 0.164, the time to expiration in years 
K = 50, the strike price 
sigma = 25%, the implied volatility

First, we need to calculate d1 and d2:

d1 = [ln(S/K) + (r - q + sigma^2/2)*T] / [sigma*sqrt(T)] 
    = [ln(48/50) + (0.07 - 0.02 + 0.25^2/2)*0.164] / [0.25*sqrt(0.164)]
    = -0.4514

d2 = d1 - sigma*sqrt(T)
    = -0.4514 - 0.25*sqrt(0.164)
    = -0.6596

Using d1 and d2, we can calculate the price of the call option:

C = 48*e^(-0.02*0.164)*N(-0.4514) - 50*e^(-0.07*0.164)*N(-0.6596)
  = 1.340 - 0.020
  = 1.320

After 5 days, the stock price rises to $50.00, which means the call option is now worth:

C' = 50*e^(-0.07*55/365)*N(0.2319) - 50*e^(-0.07*55/365)*N(-0.4266)
   = 2.294 - 1.350
   = 0.944

The profit or loss for the short call position is the difference between the initial option price and the updated option price:

Profit or loss = C - C'
               = 1.320 - 0.944
               = -$0.376
The answer is B because as a short call position, a price increase in the underlying stock price would result in a loss for the position.

Assume That a $50 Strike Call Pays a 2