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中文题目In a one-period binomial model, S0=100, Su=120, Sd=90, and the simple risk-free rate is 0. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.
打开 →In a one-period binomial model, S0=50, Su=65, Sd=45, and the simple risk-free rate is 0.05. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.
打开 →In a one-period binomial model the stock has S0=100 and goes to Su=130 or Sd=90, with risk-free rate 0. A call struck at K=100 trades at price 12. Back out the implied risk-neutral probability of the up state from this option quote.
打开 →A one-step binomial tree has up factor u=1.15, down factor d=0.88, continuously compounded rate r=0.05, and Δt=0.5. Compute the risk-neutral probability of an up move.
打开 →On the same binomial tree, an analyst estimates a real-world up probability of 0.65 from historical data, while the risk-neutral up probability is 0.52. Which probability should be used to price a derivative by discounted expectation, and what governs the gap between the two?
打开 →Why would it be a category error to judge a forecasting model's backtest solely against risk-neutral densities implied by option prices?
打开 →Why should the binomial-tree risk-neutral probability not be interpreted as your actual forecast of an up move?
打开 →A one-step binomial model gives next-step option payoffs 1 in the up state and 9 in the down state, with risk-neutral up probability 0.5 and interest rate 0.00% for the step. The option's immediate exercise value today is 4.5. What are the European and American values today?
打开 →In a one-step risk-neutral model, the terminal payoffs are 20 and 2, the up probability is 0.55, the step rate is 2.00%, and immediate exercise today is worth 10.2. What is the American value today, and what is its premium over the matching European?
打开 →A one-step binomial model gives next-step option payoffs 0 in the up state and 14 in the down state, with risk-neutral up probability 0.45 and interest rate 5.00% for the step. The option's immediate exercise value today is 7. What are the European and American values today?
打开 →derivatives · black-scholes · gbm · risk-neutral · stochastic-calculus · pde · delta-hedging · no-arbitrage
打开 →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 →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 →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 →A desk uses the simplified risk-neutral drift relation mu_Q = r - lambda*kappa for a jump-diffusion. If r = 3.00%, lambda = 1.2, and mu_Q = 0.60%, what jump compensator kappa is implied?
打开 →A risk-neutral jump-diffusion uses mu_Q = r - lambda*kappa. If r = 4.00%, lambda = 0.8, and kappa = 1.00%, what is mu_Q?
打开 →A desk uses the simplified risk-neutral drift relation mu_Q = r - lambda*kappa for a jump-diffusion. If r = 1.50%, lambda = 2, and mu_Q = -0.30%, what jump compensator kappa is implied?
打开 →A stock has spot 90 and 1-year discounted risk-neutral expectation E[e^{-rT}S_T] = 88.218. What continuous dividend yield q is implied?
打开 →Under risk-neutral pricing, spot is 120, risk-free rate is 4%, dividend yield is 1.5%, and maturity is 2 years. What is E[S_T]?
打开 →In a one-step risk-neutral model, the terminal payoffs are 0 and 16, the up probability is 0.5, the step rate is 4.00%, and immediate exercise today is worth 9. What is the American value today, and what is its premium over the matching European?
打开 →A one-step binomial tree has spot=100, strike=100, u=1.1, d=0.9, rate r=0.05, continuous dividend yield δ=0.02, Δt=1. Using the dividend-adjusted risk-neutral probability, price the European call.
打开 →A one-step trinomial tree uses spot 100, strike 102, multipliers u=1.12, m=1, d=0.9, risk-neutral probabilities (0.25, 0.5, 0.25), rate 0.03, and Δt=1. What is the European call price?
打开 →A one-step trinomial tree uses spot 80, strike 75, multipliers u=1.1, m=1, d=0.92, risk-neutral probabilities (0.3, 0.45, 0.25), rate 0.04, and Δt=0.5. What is the European call price?
打开 →In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 84.13% and you may use the standard-normal identity N(--1) = 0.8413. What d2 is implied?
打开 →In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 15.87% and you may use the standard-normal identity N(-1) = 0.1587. What d2 is implied?
打开 →In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 30.85% and you may use the standard-normal identity N(-0.5) = 0.3085. What d2 is implied?
打开 →In the one-period Merton model, the risk-neutral default probability is N(-d2). Suppose the model-implied default probability is 69.15% and you may use the standard-normal identity N(--0.5) = 0.6915. What d2 is implied?
打开 →周五下午两点四十，上海某私募基金的期权做市账户上挂着 200 张沪深300 ETF（510300）近月平值 call，对应 Delta 暴露约 +1.8 万股。屏幕上当日隐含波动率（implied volatility, IV）抬升了 2 个 vol，但标的 ETF 几乎没动。Pricing 同学甩出一个问题：「下一张 call 的理论价，我应该用今天的真实...
打开 →周三上午十点半，一位上海私募的衍生品交易员盯着两块屏幕：一块是 SSE 50ETF（510050）期权链，本周到期、行权价 2.55 的 call 中间价 0.0185；另一块是他自己的 Python 估值脚本，输出 0.0192。差 0.0007——折成单张合约 ¥70（合约乘数 10000），全市场未平仓约 1.2 万张就是 ¥84 万的潜在分歧。屏幕上...
打开 →周一早盘的两张价表 周一早上九点二十，一家做股指增强的私募衍生品桌。前四节课你已经把测度从 公式 换到了 公式，把沪深300股指期货（CFFEX IF 主力合约）的无套利价格写成了 公式。现在风控来催价表：上证 50ETF 期权的平值合约要在十分钟后挂出做市报价。第 4 课的风险中性（risk neutral）公式告诉了你期望的形式，却留下两个未结清的缺口：...
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