Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 38 / 4 / a

Buy one lower-strike European call option and sell one higher-strike European call option. The initial cost is $C(K_i)-C(K_{i+1})<0$, so the strategy releases strictly positive cash. Its terminal payoff isfor every stock price. Thus it is an arbitrage: a positive initial receipt accompanies a nonnegative terminal obligation. One may consume the receipt immediately, or hold it in cash to make a zero-initial-capital strategy with strictly positive terminal wealth. This is the vertical-spread arbitrage for increasing call prices.