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Why is buying a straddle "long volatility"?

Asked at Akuna, Optiver

A stock trades at 5050. You buy the 5050-strike call and the 5050-strike put (same expiry), paying \6$ total premium.

Describe your P&L at expiry. Why is this position called "long volatility"? What are your risks as the stock moves before expiry?

Show a hint

Draw the payoff: what do you collect at expiry as a function of the final stock price STS_T?

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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