derivatives — Quantitative Finance Practice Questions

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1. If the underlying stock price S moves by +$2.00 over a very short interval, what is the estimated second-order
2. 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
3. When pricing a 'Digital' (or Binary) call option near expiry with the spot price very close to the strike, why
4. In the context of the Black-Scholes PDE, the Greek 'Theta' (Theta) measures the sensitivity of the option pric
5. When calibrating a Heston stochastic volatility model, a pra… — Does this calibration satisfy the Feller condi
6. Based on put-call parity, what is the arbitrage-free relationship?
7. Given a continuously compounded risk-free rate of 5%, what is the price of the corresponding European put opti
8. If the risk-free growth factor is e^rT = 1.02, what is the risk-neutral probability p^* of an upward move?
9. What is the value of the d_1 parameter in the Black-Scholes formula?
10. If the terminal nodes for the stock are 132.69, 100.00, and 75.36, what is the estimated value of the put toda
11. What is the minimum stock price move (either direction) required in one day for the trader to break even?
12. A trader buys a bull call spread by purchasing a call at K_1… — What is the maximum possible profit for this s
13. If the underlying asset moves by $3 in one day, what is the approximate net profit or loss for the day?
14. Consider a European call and put on a non-dividend-paying stock with S_0 = $60, K = $58, T = 0.5, and r = 4%.
15. If the risk-free growth factor over the period is 1.02, what is the risk-neutral probability p^* of an up move
16. Given S_0 = 50, K = 52, r = 4%, T = 0.5, and a risk-neutral probability of finishing in-the-money of 42%, what
17. If the stock price is $50, the strike is $52, expiry is 6 months, the rate is 4%, and the volatility is 35%, w
18. What is the risk-neutral value of a European put with a strike of $100?
19. If the risk-free growth factor over the period is 1.02, what is the risk-neutral probability p^* of an up move
20. If their correlation is ρ = 0.40, what is the 'spread volatility' hatσ required to price an exchange option be
21. A trader is long 50,000 shares worth of options with a per-share gamma of Gamma = 0.04 and a daily theta of Th
22. If the underlying asset moves by Δ S = $1.50 over one day, and the risk-free rate is negligible, what is the e
23. As the time to expiry T approaches zero with the spot price S very close to the strike K, what happens to the
24. A desk is pricing a binary cash-or-nothing call option that pays $100 if the stock price at maturity T is abov
25. According to Put-Call Parity (C - P = S_0 - Ke^-rT), is there an arbitrage opportunity?
26. For a calibration where κ = 2.0, θ = 0.04, and xi = 0.5, does the Feller condition hold?
27. As the option approaches expiry while the stock price is very close to the strike, which of the following best
28. Assuming the same market conditions, which statement is generally true?
29. If the risk-neutral probability p = 0.5539 and the discount factor per step is e^-0.025, what is the value of
30. In the Black-Scholes-Merton PDE, which parameter's absence confirms the principle of risk-neutral valuation?