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I buy an OTM strike the price converge towards the selected strike price premium increase at a rate of delta does the rate of the increase slow down due to gamma?

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  • This might be more at home n the Quants discussion than here. When people start using Greek letters to describe their investment idea, it's all Greek to me.
    – keshlam
    Dec 22, 2016 at 14:38

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If we assume constant volatility, gamma increases as the stock gets closer to the strike price. Thus, delta is increasing at a faster rate as the stock reaches closer to ITM because gamma is the derivative of delta. As the stock gets deeper ITM, the gamma will slow down as delta reaches 1 or -1 (depends if a call or a put). Thus, the value of the option will change depending upon the level of the delta. I am ignoring volatility and time for this description.

See this diagram from Investopedia: Gamma

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