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Answer: $2.30 (max risk) and uncapped (max reward)
A long straddle consists of buying both a call and a put with the same strike and maturity. The maximum loss is the total premium paid. Using put-call parity for an ATM option with \(S=K=20\), \(r=4\%\), and \(T=0.25\): \[ P = C + Ke^{-rT} - S = 1.25 + 20e^{-0.04\times 0.25} - 20 \approx 1.05 \] So the total cost of the straddle is approximately: \[ 1.25 + 1.05 = 2.30 \] That is the maximum loss. A long straddle has uncapped upside because either the call or the put can gain substantially if the stock moves sharply in either direction.
Author: Manit Arora
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Question 185.1. The price of a stock is currently $20.00. A three-month (T = 0.25 years) ATM call option on the stock with a strike at $20.00 costs $1.25. The riskless rate is 4.0%. If an investor purchases a STRADDLE (i.e., bottom straddle) that includes this call option, what is the investor’s maximum risk (loss) and maximum reward (payoff) potential, respectively, without regard to time value of money?
A
zero (max risk) and uncapped (max reward)
B
$0.80 (max risk) and $9.90 (max reward)
C
$1.25 (max risk) and $17.70 (max reward)
D
$2.30 (max risk) and uncapped (max reward)
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