Answer-first summary for fast verification
Answer: $23.20
**Correct answer: C ($23.20)** For an asset-or-nothing call, the payoff is the stock itself if the option finishes in the money. Under Black-Scholes, its value is: \[ \text{Asset-or-nothing call} = S_0 e^{-qT} N(d_1) \] Since the stock pays no dividend, \(q=0\), so: \[ 40.00 \times 0.580 = 23.20 \] You can also confirm this using the relationship: \[ C = S_0 N(d_1) - Ke^{-rT}N(d_2) \] so: \[ S_0N(d_1) = C + Ke^{-rT}N(d_2) \approx 3.20 + 20.00 = 23.20 \]
Author: Manit Arora
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Question-413.2. Assume an underlying non-dividend-paying stock has a current price of $40.00 with volatility of 25.0% per annum while the riskfree rate is 4.0% per annum. The price of a six-month, at-the-money (maturity = 0.5 years, strike = $40.00) call option on the stock is $3.20 where N(d1) = 0.580 and N(d2) = 0.510. Which is NEAREST to the price of a binary asset-or-nothing call option with the same strike price and maturity?
A
$3.20
B
$20.00
C
$23.20
D
$40.00
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