Explanation:
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.
Using put-call parity for a non-dividend-paying stock:
Given:
So the total straddle premium is:
For a long straddle:
So the trader makes a positive profit only if the stock price at expiration is below about $35 or above about $55.
C. Stock to fall outside the interval {$35.00 to $55.00}.
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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