Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-38/4/a/solution

Buy one lower-strike European call option and sell one higher-strike European call option. The initial cost is , so the strategy releases strictly positive cash. Its terminal payoff is
for 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.

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