Upper bound on a 5/10 bull call spread

Question

A stock is priced at $7$ . You want to value a bull call spread (long the $5$ call, short the $10$ call) but have no option prices; you only know the discount factor to expiry is $0.9$ . What is the tightest upper bound on the spread's price?

Short answer

$4.5$ . The spread's payoff never exceeds the strike gap $5$ , so five riskless bonds dominate it everywhere. That caps the price at $5\times0.9=4.5$ .

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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