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Quantitative Finance

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  • $\begingroup$ This may make more intuitive sense to you if you consider how the option's price appreciates (or depreciates) relative to the stock price as the stock price moves up (or down) relative to the strike. i.e. Going from out-of-the-money to at-the-money to in-the-money or vice versa. $\endgroup$ Commented Mar 9, 2017 at 19:52
  • $\begingroup$ It seems to me you are on the right track, but I couldn't follow all the steps. You might plot $\frac{\Delta}{c}$ graphically to see how it varies with S as a check on your algebraic reasoning. $\endgroup$ Commented Mar 11, 2017 at 20:37