2-Unit Call Spread at Strike 19
Two Unit Call Spread Strike Nineteen is a medium quant interview question on Option Pricing, reported to have been seen at Old mission and Optiver.
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This quant interview question is about pricing a derivative whose payoff depends on the product of two discrete random variables. It embeds an options chain on a simple but nontrivial underlying, forcing you to connect probability, expectation, and option payoffs in a concrete setting. In the context of quant prep, it sits at the intersection of basic probability and derivative pricing intuition.
It trains your ability to translate a payoff into an expected value using discrete probability, under time pressure and with mental arithmetic. You must quickly identify which outcomes matter, structure them coherently, and keep track of payoffs and probabilities without getting lost in the combinatorics. It also reinforces comfort with option-style payoff functions.
This matters for quant interviews because market making requires fast, approximate pricing of options on unusual underlyings. Interviewers want to see if you can produce a coherent, defensible market on the fly, while staying numerate, organized, and risk-aware.
What it tests
Whenever you are asked to price a derivative whose payoff depends on a finite set of discrete outcomes, the core structure is to enumerate all possible outcomes, identify those that yield a nonzero payoff, and weight each by its probability to compute the expected value. This is the law of the unconscious statistician: the expected value of a function of a random variable is the sum over all possible outcomes of the function's value at that outcome times its probability. The reason this works is that expectation is linear and respects the underlying probability distribution, regardless of how complicated the payoff function is. For options, the payoff is typically max of zero and some function (like the difference between the outcome and the strike), so only outcomes above the strike matter. This approach generalizes to any discrete random variable and any function of its outcomes, making it a universal tool for fair value calculations in finite probability spaces.
Practise this question with written feedback, or hear it in a spoken mock interview.
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