by **jess8** » Mon Jan 17, 2011 2:27 pm

Thank you mj. I plotted the graph using excel and here is how I looked at the problem.

(a). the change of the delta-hedged option (call) is dV = 0.5*gamma*(dS)^2

- here I assumed time didn't change hence there is no theta

- gamma and delta are both valued at the original spot (i.e. 100 in the exercise)

(b). consequently, the change of call option value is just due to gamma (when dS is small at least).

In my graph, I calculated

(i). original call value at the original spot (let's say it's V_ref)

(ii). call values due to different spot values (V_new)

(iii). the change of call value (V_new - V_ref), one for each new spot value

(iv). calculated (dV = V_new - V_ref - delta*dS)

(v). finally plotted the the dV vs dS graph.

Is this right? I also calculated 0.5*gamma*(dS)^2, and plotted its graph vs dS. As dV should be just this 0.5*gamma*(dS)^2 plus some higher order terms. It turned out the gamma graph is much steeper than the dV vs dS graph. I think this is due to the omission of higher order terms.. or I might have missed something...

thanks, jess