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Determined strictly with the Black-Scholes model, the price of a stock option will rise significantly when the underlying stock enters a period of volatility.

Determined strictly by the Black-Scholes model, the price of a stock option will rise significantly when the underlying stock enters a period of volatility.

Like many verbs, the passive form of the verb "to determine," including the passive participle, take the preposition "by" for the actor.

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