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Gamma-scalping a round trip

MediumFinance & Derivatives~3m

You hold a delta-hedged long option position with gamma Γ=0.10\Gamma = 0.10 per share (constant over the range in play). The stock ticks up $2, you rehedge, then it ticks back down $2 to where it started, and you rehedge again. Ignoring theta and financing, what is your total realized hedging P&L over this round trip, in dollars per share (to two decimals)?

Show hints (2)+
  1. Each rehedged move earns 12Γ (dS)2\tfrac12\Gamma\,(dS)^2.
  2. The down-leg depends on (dS)2(dS)^2 too, so it adds to the up-leg - they don't cancel.

Answer

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0.4 (± 0.001)

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