Coding and numerical round for research and developer roles.
Price an option by simulation
The question
How would you price a European call by Monte Carlo, and how do you make the error small enough to be useful?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
Simulate terminal prices, average the discounted payoff, and cut variance rather than only adding paths.
Draw standard normals, form terminal prices under the risk-neutral dynamics, average max(S - K, 0) and discount.
Error falls as 1/sqrt(n), so four times the paths for half the error. That is expensive, which is why variance reduction matters more than raw path count.
Antithetic variates pair each draw with its negation, and a control variate uses a related payoff with a known closed form to absorb most of the noise.
Also mention that for a plain European call you would not use Monte Carlo at all, since a closed form exists. Knowing when not to simulate is part of the answer.
What it is testing
Numerical judgement, not just the ability to write a loop.
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Preparing properly
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