题目5541 · 数理金融
Black-Scholes Call 1
Under Black-Scholes with spot 100, strike 100, risk-free rate 0.03, dividend yield 0, volatility 0.2, and maturity 1, what is the European call price?
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中文题目题目5542 · 数理金融
Black-Scholes Call 2
Under Black-Scholes with spot 95, strike 100, risk-free rate 0.04, dividend yield 0.01, volatility 0.25, and maturity 0.5, what is the European call price?
打开 →题目5543 · 数理金融
Black-Scholes Call 3
Under Black-Scholes with spot 120, strike 110, risk-free rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what is the European call price?
打开 →题目5546 · 数理金融
Black-Scholes Put 1
Under Black-Scholes with spot 100, strike 100, risk-free rate 0.03, dividend yield 0, volatility 0.2, and maturity 1, what is the European put price?
打开 →题目5547 · 数理金融
Black-Scholes Put 2
Under Black-Scholes with spot 95, strike 90, risk-free rate 0.04, dividend yield 0.02, volatility 0.22, and maturity 0.5, what is the European put price?
打开 →题目5548 · 数理金融
Black-Scholes Put 3
Under Black-Scholes with spot 120, strike 130, risk-free rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5, what is the European put price?
打开 →题目5885 · 数理金融
Tree Versus Black-Scholes Convergence
A one-step CRR binomial tree prices an at-the-money one-year European call at 9.95, while the Black-Scholes value with the same spot, strike, rate and volatility is 8.43. By how much does the coarse tree overprice the option, and what single change to the tree would most directly
打开 →题目4657 · 数理金融
Assumption Breakdown Diagnostic 17
If jump risk becomes larger while diffusive volatility is unchanged, what happens to the credibility of a pure Black-Scholes delta hedge?
打开 →题目4658 · 数理金融
Assumption Breakdown Diagnostic 18
If vol-of-vol rises materially, what usually happens to the plausibility of a single constant-volatility Black-Scholes description?
打开 →题目4659 · 数理金融
Assumption Breakdown Diagnostic 19
If market liquidity deteriorates sharply, which Black-Scholes assumption becomes more dangerous to ignore?
打开 →题目4660 · 数理金融
Assumption Breakdown Diagnostic 20
Why can longer-dated options expose Black-Scholes assumption failures more visibly than very short-dated options?
打开 →题目4651 · 数理金融
Assumption Breakdown Scenario 11
Observed index options suddenly show a much steeper downside skew after crash fear rises. Which Black-Scholes assumption is being stressed most directly?
打开 →题目4652 · 数理金融
Assumption Breakdown Scenario 12
Why do jumps create a particularly sharp failure mode for Black-Scholes delta hedging?
打开 →题目4653 · 数理金融
Assumption Breakdown Scenario 13
Why is 'we hedge daily' not a small implementation detail relative to Black-Scholes continuous hedging?
打开 →题目4654 · 数理金融
Assumption Breakdown Scenario 14
Why can funding spreads and stock-borrow costs break the clean Black-Scholes replication logic even if volatility were truly 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5551 · 数理金融
Forward Form And Exercise Probability 1
A stock has spot 100, strike 100, rate 0.03, dividend yield 0.01, volatility 0.2, and maturity 1. Under Black-Scholes, what are the forward price F_0,T and the risk-neutral probability that the call finishes in the money?
打开 →题目5552 · 数理金融
Forward Form And Exercise Probability 2
A stock has spot 95, strike 100, rate 0.04, dividend yield 0.02, volatility 0.25, and maturity 0.5. Under Black-Scholes, what are the forward price F_0,T and the risk-neutral probability that the call finishes in the money?
打开 →题目5553 · 数理金融
Forward Form And Exercise Probability 3
A stock has spot 120, strike 110, rate 0.02, dividend yield 0, volatility 0.18, and maturity 1.5. Under Black-Scholes, what are the forward price F_0,T and the risk-neutral probability that the call finishes in the money?
打开 →题目4851 · 数理金融
Infer Rate From Crank-Nicolson Off-Diagonals 11
Under the common Black-Scholes Crank-Nicolson convention alpha_i = 0.25*Delta_t*(sigma^2*i^2 - r*i) and gamma_i = 0.25*Delta_t*(sigma^2*i^2 + r*i). A grid dump reports i=2, Delta_t=0.5, alpha_i=0.0125, and gamma_i=0.0275. What risk-free rate r is implied?
打开 →题目2312 · 数理金融
Jump-Risk Trading Intuition 2
Why can a Black-Scholes delta hedge look fine most days and still fail violently under jump risk?
打开 →题目4601 · 数理金融
Martingale Scenario 11
Why do d1 and d2 appear as two different normal arguments in the martingale derivation of a Black-Scholes call?
打开 →题目4603 · 数理金融
Martingale Scenario 13
Why should the martingale route and the PDE route give the same Black-Scholes price?
打开 →题目4575 · 数理金融
PDE Coefficient Inversion 10
In a candidate Black-Scholes PDE, the coefficient on V is -0.06. What risk-free rate r is implied?
打开 →题目4571 · 数理金融
PDE Coefficient Inversion 6
In a candidate Black-Scholes PDE, the coefficient on S V_S is 0.015 and the risk-free rate is 0.04. What continuous dividend yield q is implied?
打开 →题目4572 · 数理金融
PDE Coefficient Inversion 7
In a candidate Black-Scholes PDE, the coefficient on S^2 V_SS is 0.03125. What volatility sigma is implied?
打开 →题目4573 · 数理金融
PDE Coefficient Inversion 8
In a Black-Scholes PDE, the coefficient on S V_S is 0.02 and the dividend yield is 0.01. What risk-free rate r is implied?
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