Harold owns 10,000 shares of IBM at $54.50 per share.He writes $55 strike covered call on all the shares.Assume = 0.14,σ = 0.18,rf = 0.04,and the options expire in 90 days.What is the value at risk for 1 day,using the delta approximation at a 95% confidence level?
A) $4,717
B) $5,717
C) $6,717
D) $7,717

Question

Harold owns 10,000 shares of IBM at $54.50 per share.He writes $55 strike covered call on all the shares.Assume  = 0.14,σ = 0.18,rf = 0.04,and the options expire in 90 days.What is the value at risk for 1 day,using the delta approximation at a 95% confidence level?
A) $4,717 
B) $5,717 
C) $6,717 
D) $7,717

Quizplus · Accepted Answer

To calculate the value at risk using the delta approximation, we first need to calculate the delta of the covered call option. 
Delta of the call option = 0.60 (using Black-Scholes model)
As the option is sold, the delta of the covered call = -0.60

Now, we need to calculate the value at risk for 1 day at a 95% confidence level:
Value at Risk = Delta x Stock Price x Standard Deviation x z-value
where z-value for 95% confidence level = 1.645

Stock Price = $54.50
Delta = -0.60
Standard Deviation = σ x sqrt(time) = 0.18 x sqrt(90/365) = 0.088
z-value = 1.645

Putting all these values in the formula, we get:
Value at Risk = -0.60 x $54.50 x 0.088 x 1.645
Value at Risk = $4.717

Therefore, the answer is A.

Harold Owns 10,000 Shares of IBM at $54