General — Quantitative Finance Practice Questions

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1. If the correlation between two assets is ρ = 0.6, what is the R^2 of a linear regression of one asset's return
2. For a standard Brownian motion W_t, what is the expected value of W_t^2?
3. If the risk-neutral probability of an up move is p = 0.6, what is the expected stock price at the end of two s
4. When calibrating a Heston stochastic volatility model, a pra… — Does this calibration satisfy the Feller condi
5. Based on put-call parity, what is the arbitrage-free relationship?
6. 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
7. Assuming 252 trading days in a year, what is the annualized historical volatility?
8. Under Girsanov's Theorem, what does a change of probability measure primarily alter in a stochastic process dr
9. Two assets are 'cointegrated'. What does this imply for a pairs-trading strategy that 'correlation' alone does
10. If the investor's coefficient of relative risk aversion is γ = 4, what is the Merton optimal fraction (π^*) to
11. If the flat yield curve is at 4% (continuously compounded), what is the bond's price?
12. What is the fair no-arbitrage price for a six-month (T = 0.5) forward contract?
13. When pricing a 'Digital' (or Binary) call option near expiry with the spot price very close to the strike, why
14. Calculate the price of a zero-coupon bond that pays $1000 in two years, given that the one-year discount facto
15. According to the Merton portfolio problem, what is the optimal fraction π^* of wealth to hold in the risky ass
16. If yesterday's return was 2% and the conditional variance was 0.0001, what is the updated conditional volatili
17. What is the estimated OLS slope hatβ?
18. In the context of the HJM framework, what is the primary lesson regarding the drift of the forward rate curve?
19. In the context of the Black-Scholes PDE, the Greek 'Theta' (Theta) measures the sensitivity of the option pric
20. A portfolio has a daily expected return of 0.05% and a daily volatility of 1.2%. Using the parametric method a
21. What is the defining property of the 'Cumulative Distribution Function' F(x)?
22. Which 'standardized moment' should they measure to quantify this?
23. In the Vasicek short-rate model dr_t = κ(θ - r_t) dt + σ dW_t, what happens to the drift when the current rate
24. If the underlying stock price S moves by +$2.00 over a very short interval, what is the estimated second-order
25. As the number of assets n approaches infinity, what happens to the total portfolio variance?
26. If the slope β is positive, what is the correlation coefficient ρ between x and y?
27. Under the geometric Brownian motion model with μ = 0.12, σ = 0.30, and S_0 = 100, what is the median stock pri
28. Given a continuously compounded risk-free rate of 5%, what is the price of the corresponding European put opti
29. If the risk-free growth factor is e^rT = 1.02, what is the risk-neutral probability p^* of an upward move?
30. If the terminal nodes for the stock are 132.69, 100.00, and 75.36, what is the estimated value of the put toda