Hard Quantitative Finance Practice Questions

90 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. Using the standard approximation, what is the fair CDS spread s in basis points?
2. If the correlation between the original payoff X and the antithetic payoff X' is ρ = -0.7, by what factor is t
3. If the trader increases their risk aversion λ, what is the effect on the execution trajectory?
4. A symmetric 2 × 2 covariance matrix has eigenvalues λ_1 = 0.… — What does this imply about the validity of the
5. What is the estimated percentage price change?
6. In the Merton structural model, a firm has assets worth 150M with an asset volatility of 30%. It has a zero-co
7. According to the Merton portfolio problem, what is the optimal fraction of wealth to invest in the risky asset
8. By what factor is the variance of the antithetic estimator reduced compared to two independent paths?
9. If the current conditional variance is σ_t^2 = 0.00025, what is the forecasted conditional variance for two st
10. If Asset X is observed to return 23%, what is the conditional expected return of Asset Y?
11. As the time to expiry T approaches zero with the spot price S very close to the strike K, what happens to the
12. To reduce the standard error to $0.05 using only a larger sample size, how many total paths are required?
13. What is the variance of the number of heads (H) observed, using the Law of Total Variance?
14. Using the Merton structural model for credit risk, a firm has assets A_0 = 200 million and total debt D = 150
15. According to Put-Call Parity (C - P = S_0 - Ke^-rT), is there an arbitrage opportunity?
16. For a calibration where κ = 2.0, θ = 0.04, and xi = 0.5, does the Feller condition hold?
17. What is the primary advantage of using a 'control variate' in Monte Carlo simulation for pricing an arithmetic
18. Which property of a Gaussian copula most significantly distinguishes it from a t-copula in the context of fina
19. Why is the Cholesky Decomposition frequently used in multivariate Monte Carlo simulations of correlated asset
20. If the risky asset has an excess return (μ - r) of 7% and a volatility of 20%, what percentage of wealth shoul
21. According to the Merton portfolio problem, what is the optimal fraction π^* of wealth to hold in the risky ass
22. A 5-year bond with a face value of $1,000 and an annual coupon of 6% is priced at par. If the yield increases
23. As the option approaches expiry while the stock price is very close to the strike, which of the following best
24. A practitioner is calibrating a Heston stochastic volatility… — Does this calibration satisfy the Feller condi
25. If yesterday's volatility was 1.5% and the return was -2%, what is the predicted annualized volatility for the
26. What is the 'volatility of the spread' hatσ used in the Black-Scholes calculation?
27. What is the half-life of a deviation in the spread, and what does this imply for the strategy?
28. Using the principle of in-out parity, what is the fair value of the corresponding down-and-in (D&I) call?
29. For a risk-averse trader who must liquidate a large block of shares, what is the characteristic shape of the o
30. In the Heath-Jarrow-Morton (HJM) framework for modeling the term structure of interest rates, what is the sign

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