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Answer: Stock to fall outside the interval {$35.00 to $55.00}; i.e., either below $35.00 or above $55.00
A **long straddle** profits when the underlying moves **far enough away** from the strike price in either direction. The trader pays the total premium for the call plus the put. ### Step 1: Find the call price Using put-call parity for a non-dividend-paying stock: \[ C = P + S_0 - Ke^{-rT} \] Given: - \(P = 3.50\) - \(S_0 = 47.00\) - \(K = 45.00\) - \(r = 3\%\) - \(T = 0.75\) \[ Ke^{-rT} = 45e^{-0.03(0.75)} \approx 43.99 \] \[ C \approx 3.50 + 47.00 - 43.99 = 6.51 \] So the total straddle premium is: \[ 6.51 + 3.50 = 10.01 \] ### Step 2: Compute break-even prices For a long straddle: \[ \text{Lower break-even} = K - \text{premium} \approx 45 - 10.01 = 34.99 \] \[ \text{Upper break-even} = K + \text{premium} \approx 45 + 10.01 = 55.01 \] So the trader makes a positive profit only if the stock price at expiration is **below about $35** or **above about $55**. ### Correct choice **C. Stock to fall outside the interval {$35.00 to $55.00}.**
Author: Manit Arora
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Q-724.1. A stock with a volatility of 31.0% is currently trading at $47.00 while the risk-free rate is 3.0%. An investor purchases a European straddle with a strike price of $45.00: a straddle is a call and a put on the same stock with identical strike prices and expiration dates. The straddle expires in nine months (0.75 years). The price of the put is $3.50. Among the following choices, which best summarizes the final stock price required (in nine months, at expiration) in order for the trader to realize at least a positive net PROFIT on this trade?
A
Stock to stay inside the interval {$35.00 to $55.00}; i.e., both above $35.00 and below $55.00
B
Stock to stay inside the interval {$37.00 to $57.00}; i.e., both above $37.00 and below $57.00
C
Stock to fall outside the interval {$35.00 to $55.00}; i.e., either below $35.00 or above $55.00
D
Stock to fall outside the interval {$40.00 to $54.00}; i.e., either below $40.00 or above $54.00
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