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New · Free interview workbook50 FX Derivatives Problems for Quant Interviews
A genuine LaTeX-typeset practice workbook for pricing, strats, model validation, market risk and quantitative research interviews. All 50 questions appear first, followed by complete worked solutions in the appendix.
50 problemsComplete solutionsFormula reference17-page PDF
- Forwards, swaps & NDFs
- Garman–Kohlhagen & Greeks
- Delta conventions & smile
- Barriers, quanto & exotics
- Collateral & cross-currency basis
- Monte Carlo, PDE & validation
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Game Theory & Backward Induction
100 rational, ferocious tigers and 1 sheep are on an island. If a tiger eats the sheep, the tiger turns into a sheep (and can now be eaten by other tigers). Eating is the only way to satisfy hunger, but surviving is their highest priority. Does the first tiger eat the sheep?
Classic quantitative interview puzzle tested at D.E. Shaw, Jane Street, and Two Sigma.
Desk Hint:
Use backward induction: what happens if there is only 1 tiger on the island? What if there are 2 tigers? 3 tigers? Notice the even/odd parity.
Rigorous Solution & Intuition:
The first tiger does NOT eat the sheep. The sheep survives unharmed.
Backward Induction Proof:
• 1 Tiger: The tiger eats the sheep immediately because there are no other tigers left to eat it.
• 2 Tigers: Neither tiger eats. If Tiger A eats the sheep, Tiger A becomes a sheep with 1 tiger left (Tiger B), which would immediately eat Tiger A. Since survival is priority #1, neither tiger eats.
• 3 Tigers: The first tiger eats the sheep. It knows that once it becomes a sheep, there are 2 tigers left, and as proven above, 2 tigers will never eat the sheep.
• General Parity Rule: For any odd number of tigers (1, 3, 5, ...), the first tiger eats the sheep. For any even number of tigers (2, 4, 6, ..., 100), no tiger will make the first move. With 100 tigers, the sheep is completely safe!