This question was asked in FRM exam 1999. I tried a lot but couldn't understand, please help.A risk manager wants to examine the effects of price changes in the underlying on a put option on 5 contracts of live cattle futures (contract size =40,000 lbs). The Greeks are as follows: Delta = -0.7 Gamma = 2.5 contracts/dollarVega = $450 / % implied volatilityTheta = $200 / day.The risk manager wants to see the effect on the value of the option due to first and second order price movements if the price of cattle were to rise from 64.3 cents per pound to 69.5 cents per pound immediately after she bought the option. The correct answer is that the effect would be a decrease of $7,145.

change due to delta: -0.7 x 5 x 40,000 x (0.695 - 0.643) = -7280gamma = 2.5 contracts per dollar = 100,000 lbs of cattle per dollarso change due to gamma: 1/2 x 100,000 x (.695 - 0.643)^2 = 135.20 total instantaneous change in MTM assuming no change in implied vol: 135.20 minus 7280 = -7144.80

yes, it solves in the same fashion as we use duration and convexity to tackle the bond price change when interest rate changes.Acutally, Manishs, you can get the followings:dC=delta*dS+1/2*gamma*(dS)^2+theta*dt+higher order errors. (dt is set to zero for this immediately change after purchasing)Enjoy your exam,Jin

Hi Kurve,Thank you very much.Warm RegardsManish

Hello Jin,Thanks for supplying the equation. Warm RegardsManish