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A Monte Carlo put

Expected valueEasy

A put with strike $60$ pays the excess of the strike over the final price, or nothing if there is none. A simulation gives $5$ final prices: $55$ , $63$ , $48$ , $60$ , $52$ . What is the Monte Carlo estimate of its expected payoff? Answer with a number.

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Hint

Find the payoff on each path, then average all of them, zeros included.

Solution

The payoffs are $5$ , $0$ , $12$ , $0$ , $8$ , which sum to $25$ .
The estimate is $\frac{25}{5} = 5$ , so the answer is $5$ .

Answer: $5$

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