题目1410 · 脑筋急转弯
ATM Call Proxy 2
Use the desk proxy premium ~= 0.4 * S * sigma * sqrt(T). If S=120, sigma=30%, and T=0.25 years, what premium estimate results?
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中文题目题目1425 · 脑筋急转弯
Basis-Point Revenue 17
What is 7.5 bp of $640 million?
打开 →题目1405 · 脑筋急转弯
Block Trade Gross 5
A desk proxy for gross block-trade dollars is block count * average block size in dollars. If those inputs are 1250 and $14 million, what estimate results?
打开 →题目4856 · 数理金融
Call Upper Boundary
In a finite-difference grid for a European call, why is the far-right boundary often set close to S_max - K e^(-rτ) rather than to a constant?
打开 →题目5566 · 数理金融
Delta And Gamma 1
For a European call with spot 100, strike 100, rate 0.03, dividend yield 0, volatility 0.2, and maturity 1, what are Black-Scholes delta and gamma?
打开 →题目5567 · 数理金融
Delta And Gamma 2
For a European put with spot 95, strike 100, rate 0.04, dividend yield 0.01, volatility 0.25, and maturity 0.5, what are Black-Scholes delta and gamma?
打开 →题目5568 · 数理金融
Delta And Gamma 3
For a European call with spot 120, strike 110, rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what are Black-Scholes delta and gamma?
打开 →题目5570 · 数理金融
Delta And Gamma 5
For a European call with spot 150, strike 140, rate 0.03, dividend yield 0.01, volatility 0.22, and maturity 1.25, what are Black-Scholes delta and gamma?
打开 →题目5576 · 数理金融
Delta Hedge Rebalance 1
A desk is long 250 option contracts, each on 100 shares. The option delta moves from 0.42 to 0.48 after the market moves. How many shares should the desk hold before and after, and how many shares must it trade to rebalance to delta neutral?
打开 →题目5577 · 数理金融
Delta Hedge Rebalance 2
A desk is long 120 option contracts, each on 100 shares. The option delta moves from -0.31 to -0.22 after the market moves. How many shares should the desk hold before and after, and how many shares must it trade to rebalance to delta neutral?
打开 →题目2050 · 数学
Derive the Newton Update for x + a/x = b 5
Derive the Newton iteration for solving x + a/x = b.
打开 →题目4862 · 数理金融
Infer Center Node From Gamma 17
At a stock grid with Delta_S=2, the central-difference gamma is Gamma ≈ (V_{i+1}-2V_i+V_{i-1})/Delta_S^2. If V_{i+1}=11, V_{i-1}=7, and the desk wants Gamma=0.5, what center value V_i is needed?
打开 →题目4863 · 数理金融
Infer Missing Lower Node From Delta 18
At a stock grid with Delta_S=1, the central-difference delta is Delta ≈ (V_{i+1}-V_{i-1})/(2*Delta_S). If V_{i+1}=9.4 and the target delta is 0.7, what V_{i-1} is implied?
打开 →题目4861 · 数理金融
Infer Missing Upper Node From Delta 16
At a stock grid with Delta_S=5, the central-difference delta is approximated by Delta ≈ (V_{i+1}-V_{i-1})/(2*Delta_S). If V_{i-1}=12 and the desk wants Delta=0.8, what V_{i+1} is needed?
打开 →题目4858 · 数理金融
Negative Weights
Why are explicit or theta-scheme weights turning negative a warning sign for an option grid, especially near kinks?
打开 →题目4859 · 数理金融
Nonuniform Grid
Why can clustering grid points around the strike improve gamma estimates more than simply extending S_max farther out?
打开 →题目1408 · 脑筋急转弯
Prime-Broker Margin 8
A desk proxy for aggregate posted margin is clients * average posted margin. If the total is $3.128 billion and clients is 920, what average posted margin is implied?
打开 →题目4857 · 数理金融
Put Lower Boundary
Why does a European put grid often impose V(0,τ) ≈ K e^(-rτ) at the left boundary?
打开 →题目4860 · 数理金融
Too Small Truncation
If S_max is chosen too low in a call-pricing grid, what directional bias do you expect for deep in-the-money call values near the top of the grid, and why?
打开 →题目894 · 脑筋急转弯
Two-Segment Demand Total 4
A forecast splits annual support chats into Segment A with 15000 entities at 2.5 events each and Segment B with 3000 entities at 6 events each. What is the combined annual estimate?
打开 →题目5571 · 数理金融
Vega And Rho 1
For a European call with spot 100, strike 100, rate 0.03, dividend yield 0, volatility 0.2, and maturity 1, what are Black-Scholes vega and rho?
打开 →题目5572 · 数理金融
Vega And Rho 2
For a European put with spot 95, strike 90, rate 0.04, dividend yield 0.02, volatility 0.22, and maturity 0.5, what are Black-Scholes vega and rho?
打开 →题目5573 · 数理金融
Vega And Rho 3
For a European call with spot 120, strike 130, rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what are Black-Scholes vega and rho?
打开 →题目5581 · 数理金融
Vega Maturity Ranking 1
Two European calls have the same spot, strike family, rate, dividend yield, and volatility 0.3. Assume both have approximately the same d1 = 0.1, but option A has maturity 1 and option B has maturity 0.5. Which option has the larger Black-Scholes vega?
打开 →题目5582 · 数理金融
Vega Maturity Ranking 2
Two European puts have the same spot, strike family, rate, dividend yield, and volatility 0.22. Assume both have approximately the same d1 = 0.05, but option A has maturity 0.25 and option B has maturity 1. Which option has the larger Black-Scholes vega?
打开 →题目5583 · 数理金融
Vega Maturity Ranking 3
Two European calls have the same spot, strike family, rate, dividend yield, and volatility 0.18. Assume both have approximately the same d1 = 0, but option A has maturity 0.5 and option B has maturity 1.5. Which option has the larger Black-Scholes vega?
打开 →题目5584 · 数理金融
Vega Maturity Ranking 4
Two European calls have the same spot, strike family, rate, dividend yield, and volatility 0.25. Assume both have approximately the same d1 = 0.25, but option A has maturity 0.75 and option B has maturity 0.25. Which option has the larger Black-Scholes vega?
打开 →题目5585 · 数理金融
Vega Maturity Ranking 5
Two European puts have the same spot, strike family, rate, dividend yield, and volatility 0.2. Assume both have approximately the same d1 = -0.05, but option A has maturity 1.25 and option B has maturity 0.5. Which option has the larger Black-Scholes vega?
打开 →题目1413 · 脑筋急转弯
Vega Proxy 5
Use the proxy vega ~= 0.4 * S * sqrt(T). If S=95 and T=1 year, what vega estimate results?
打开 →题目5586 · 数理金融
Why Gamma And Theta Trade Off
Why do long-gamma positions often come with negative theta in vanilla options?
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