A call's move under changing delta

A call currently has delta 0.600.60. The stock rises $2, and over that move the call's delta climbs to 0.700.70 (its gamma is positive). Using the average delta across the move, estimate the increase in the call's price, in dollars to two decimals.

Show hints (2)+
  1. Delta isn't constant over the move - gamma raises it. Use the average of the two deltas.
  2. Δˉ=(0.60+0.70)/2\bar\Delta = (0.60+0.70)/2, then multiply by the $2 move.

Answer

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1.3 (± 0.001)

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Asked at: Game-Based Aptitude, EV & Betting Games

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