Market on a spread of two quoted products

Question

You are quoting product $A$ at $4$ bid, $5$ offer and product $B$ at $10$ bid, $12$ offer. What market would you make in the spread $A-B$ ? If your quote is bid $X$ , offer $Y$ , report $Y^2-X^2$ .

Short answer

$-39$ . Buying $A-B$ means buying $A$ at your bid and selling $B$ at your offer, so the bid is $4-12=-8$ ; selling it means selling $A$ at $5$ and buying $B$ at $10$ , so the offer is $-5$ . Then $25-64=-39$ .

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

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Lessons behind this question

Market Model and Risk-Neutral Valuation
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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