What assumptions support the value, and what risk changes when another trade is added? This original fictional exercise focuses on separating a modeled expected value from a quote and inventory decision. The task is to build a payoff/edge calculation and inventory explanation, not copy a confident conclusion. It is not a live recommendation, client record or employer assessment.
The inputs and the question
A market-making preparation exercise can test probability, uncertainty and inventory reasoning. This guide uses a fictional binary payoff. It is not a real market quote or a claim that a positive modeled edge is a guaranteed profit.
| Supplied item | Fictional input |
|---|---|
| Payoff if event occurs | 1 |
| Payoff otherwise | 0 |
| Assumed event probability | 62% |
| Purchase price and fee | 0.60 and 0.005 per unit |
Use the supplied inputs together. When dates, units or definitions are not given, identify the gap rather than silently filling it with a convenient assumption. An actual assignment may require more detail than this deliberately limited case.
Work through the base case
Modeled expected payoff is 0.62. Expected payoff minus price and fee is 0.62 − 0.60 − 0.005 = 0.015 per unit under the supplied probability. That expectation is not a certain trade outcome.
Question the probability estimate, adverse selection, fee convention and inventory constraints. The fair-value calculation is only one input to a quoting decision.
The arithmetic or evidence check is only one part of the answer. Explain the definition that makes it valid and what remains outside the exercise. Do not convert a result from this case into a claim about a real company, market or client.
Change the assumption and follow the consequence
At a 59% probability with the same price and fee, modeled expected edge becomes 0.59 − 0.60 − 0.005 = −0.015. Buying 20 more units at the original modeled fair value adds 12.4 of fair-value exposure, not a defined VaR.
Keep the unchanged inputs visible. State whether the change is an observed fact or a scenario you introduced. If the information needed to calculate a fuller result is missing, say what you would request instead of manufacturing precision.
The interpretation to avoid
Treating a probability estimate as certainty, ignoring the existing position or conflating expected edge with a risk limit removes the main judgment.
A useful response names the limitation without abandoning the task. Show the part you can establish, then explain the condition or document needed for the next conclusion. Being explicit about that boundary is different from refusing to reason about the case.
Build the evidence artifact
State the payoff, probability and fee conventions, then explain the uncertainty and inventory consequence. Ask what evidence would change the quote.
Answer these questions before presenting it:
- How is the event probability estimated and what could make it wrong?
- What existing position and risk constraints matter?
- What information might the counterparty have that the estimate misses?
For your own practice, write the supplied facts, your method, the base result, the changed assumption and one unresolved question on a single page. Label professional work, public-data projects and fictional exercises accurately. Remove confidential data and do not use the example to imply a decision you did not own.
What to use next
Use the market making preparation guide to connect the exercise to a readiness and next-resource decision. Compare the adjacent preparation task if your gap is different. The primary-source background supplies concept or role context; the facts and worked exercise above are original and fictional.
The existing trading playbook supports preparation; it is not a live trading strategy or employer assessment. Inspect scope before choosing support. A readable and reproducible explanation is the immediate objective; this case does not promise an interview, qualification, investment result or a particular search ranking.