medium · Quantitative Finance

A portfolio manager holds a long position in a European call option with S_0 = 100, Δ = 0.60, Γ = 0.04, and Θ = -12.60 per year.

If the stock price jumps to 102 overnight (1 day, assuming 252 trading days), which of the following is the most accurate approximation for the change in the option's value?

  1. 1.15
  2. 1.23
  3. 1.28
  4. 1.20

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