Hard Quantitative Finance Practice Questions

76 free hard-difficulty Quantitative Finance questions, drawn live from KomFi's calibrated bank. These are the items that separate top scorers — every one carries a full explanation and trap analysis once you sign in.

1. If the risk-neutral probability of an up move is p = 0.6 and the risk-free rate is zero, what is the price of
2. When calibrating a Heston stochastic volatility model, a pra… — Does this calibration satisfy the Feller condi
3. What is the minimum stock price move (either direction) required in one day for the trader to break even?
4. Consider a European call and put on a non-dividend-paying stock with S_0 = $60, K = $58, T = 0.5, and r = 4%.
5. What is the risk-neutral value of a European put with a strike of $100?
6. As the time to expiry T approaches zero with the spot price S very close to the strike K, what happens to the
7. According to Put-Call Parity (C - P = S_0 - Ke^-rT), is there an arbitrage opportunity?
8. For a calibration where κ = 2.0, θ = 0.04, and xi = 0.5, does the Feller condition hold?
9. As the option approaches expiry while the stock price is very close to the strike, which of the following best
10. If the time step is Δ t = 0.5, what is the fair price of this call option today?
11. A practitioner is calibrating a Heston stochastic volatility… — Does this calibration satisfy the Feller condi
12. A trader is short 500 European call option contracts, with each contract covering 100 shares. The per-share ga
13. A practitioner observes that the 'Volatility Smile' for equi… — Which modeling adjustment is most likely to re
14. If a Heston model is calibrated with ρ = -0.7, how would the price of an out-of-the-money (OTM) put compare to
15. In the Black-Scholes PDE, the term -rV acts as a 'decay' ter… — If an option is very deep in-the-money, how do
16. What is the formula for S'_0?
17. In the Merton structural credit model, the debt of a firm is equivalent to which of the following option posit
18. Ignoring funding and transaction costs, which statement about the trader's P&L is correct?
19. What is the precise no-arbitrage condition being violated, and where does it bite?
20. Which pair correctly captures the necessary no-arbitrage requirements?
21. In a stochastic-volatility model (e.g. Heston), a long-dated… — What is the primary financial reason for this
22. What is the half-life of a deviation in the spread, and what does this imply for the strategy?
23. For a risk-averse trader who must liquidate a large block of shares, what is the characteristic shape of the o
24. What is the long-run (unconditional) standard deviation of this spread, which is often used to set entry Z-sco
25. If the returns are normally distributed with mean 0 and standard deviation σ, what is the relationship between
26. What is the approximate speed of mean reversion κ on an annualized basis (252 business days)?
27. What is the correct quantitative reason the two cost models rank strategies differently, beyond average magnit
28. What is the equilibrium price-impact coefficient λ?
29. If the correlation between the original payoff X and the antithetic payoff X' is ρ = -0.7, by what factor is t
30. By what factor is the variance of the antithetic estimator reduced compared to two independent paths?

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