Vega of a short in-the-money call as spot falls

Question

A stock trades at $S_0 = 42$ and you have sold a call struck at $K = 36$ . Suppose the stock price now drops. How does the vega of your position change?

Reply $1$ if it goes up, $0$ if it is unchanged, or $-1$ if it goes down.

Short answer

$-1$ (vega decreases). An option's vega is largest near the money. The call is currently in the money, so a fall in $S$ toward $36$ makes the option's vega bigger in size; because you are short the call your vega is negative, so it becomes more negative.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Greeks and Numerical Sensitivities
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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