Answer-first summary for fast verification
Answer: $7.69
A box spread combines a bull spread and a bear spread to create a **fixed payoff at expiration** equal to the difference between the strikes. Here the strikes are: - Lower strike = $16 - Upper strike = $24 So the future payoff is: - $24 - $16 = **$8** Because the question asks for the **present value of the future payoff**, discount the payoff at the continuously compounded risk-free rate: - PV = $8 e^{-0.04 \times 1}$ - PV = $8 e^{-0.04}$ - PV ≈ $8(0.960789)$ = **$7.69**$ Therefore, the correct answer is **C**.
Author: Manit Arora
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Q-184.3. The stock of ACME company is currently trading at $20.00. At a strike price of $16.00, a call option costs $6.00 and a put option costs $1.37. At a strike of $24.00, a call option costs $1.20 and a put option costs $4.26. All of the options are European with one year to expiration. The risk-free rate is 4.0% per annum continuously compounded. What is the present value (PV) of the future PAYOFF of a BOX SPREAD strategy (note: while “profit” nets the initial cost, “payoff” does not net the initial cost)?
A
Zero
B
$1.15
C
$7.69
D
$8.00
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