No-arbitrage bounds for a European call

Question

For a European call on a stock that pays no dividends, what are the tightest model-free upper and lower bounds on its price?

Short answer

$\max(S-Ke^{-rT},0)\le C\le S$ . The call cannot be worth more than the stock it lets you buy, and it is worth at least zero and at least a forward struck at $K$ (by put-call parity, $C=S-Ke^{-rT}+P$ with $P\ge0$ ).

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.28, p.18; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Options, Payoffs and No-Arbitrage Bounds
No-Arbitrage Bounds and Put-Call Parity

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