I am trying to establish the relationship between put options and greeks through a general form problem. Suppose that there is a company that at market opening trades its shares at a price $p_1$.Now assume that we price a put option with a given delta $\delta$ and a given gamma $\gamma$ at a price of $p_2$. Now suppose that the stock price decreased by an amount of $\epsilon$ soon after the market opens, enough so that the value of the option increases by $p_3$. What general form will solving for $\epsilon$ take using $\gamma$ and $\delta$?

  • $\begingroup$ To a first approximation $p_3 \approx \delta\cdot\epsilon + 0.5\cdot\gamma\cdot \epsilon^2$. (If we neglect higher order terms, the passage of time $\Delta t$ and the change in IV if any.). That's just a result of the basic definition of $\delta$ and $\gamma$. $\endgroup$ – noob2 Jun 11 at 13:07

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