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Answer: $22.86
If the option premium is deferred until maturity, the buyer must repay the option premium plus interest at expiration. The call must therefore finish above: \[ K + C_0 e^{rT} \] For an ATM call with \(S=K=20\), \(\sigma=30\%\), \(r=4\%\), and \(T=1\), the Black-Scholes call value is approximately \(C_0 \approx 2.75\). Accumulating that premium to maturity gives: \[ 2.75e^{0.04} \approx 2.86 \] Thus the break-even stock price is: \[ 20 + 2.86 = 22.86 \] So the payoff becomes positive only if the stock price is above **$22.86**.
Author: Manit Arora
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Q-10.2 Assume price of an at-the-money (ATM) non dividend stock is $20 (S=20) with volatility of 30%. The riskfree rate is 4%. The term for a European call option is one year (T=1). If we convert the option into a zero-cost product by deferring payment until maturity, what stock price must be achieved to make the payoff positive?
A
$20.01
B
$22.00
C
$22.75
D
$22.86
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