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中文题目
题目4880 · 数理金融

Variance Improvement From Pairing 15

Without common random numbers, two independent estimators have standard deviations 4 and 5, so the variance of their difference would be 4^2+5^2. With pairing, the observed paired-difference standard deviation is 3. What fraction of the unpaired difference variance remains?

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题目5989 · 概率

Variance of a Count Window

Trades hit a tape as a Poisson process with rate 6 per hour. Let $N$ be the number of trades in a fixed 20-minute window. What is $\mathrm{Var}(N)$?

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题目155 · 概率

Variance of Birthday-Collision Pair Count

Continuing from the setup of the expected collision-pair count: $n$ people have independent uniform birthdays on $\{1,\ldots,d\}$. Define $X = \sum_{i<j} \mathbf{1}[B_i = B_j]$. (a) Compute $\operatorname{Var}(X)$. (b) A surprising intermediate step: show that $\operatorname{Co

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题目5982 · 概率

Variance of Fills Over a Binomial Number of Quotes

Out of $n=10$ resting quotes, each fills independently with probability $0.3$, so the number of fills $N$ is Binomial$(10,0.3)$. Each fill produces an i.i.d. PnL $X_i$ with $E[X_i]=2$ and $\mathrm{Var}(X_i)=9$, independent of which quotes fill. For the stopped sum $S_N=\sum_{i=1}

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题目5950 · 概率

Variance of the Coverage Count

4 balls are thrown independently and uniformly into 6 boxes. Let $D$ be the number of boxes that receive at least one ball. Compute $\operatorname{Var}(D)$.

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题目5996 · 概率

Variance of the Fourth Arrival Time

Packets arrive at a sensor as a Poisson process with rate 2 per minute. Let $T_4$ be the time of the 4th packet. What is $\mathrm{Var}(T_4)$, in minutes squared?

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题目194 · 概率

Variance of the Number of Occupied Urns

Four distinguishable balls are thrown independently and uniformly at random into 3 distinguishable urns. Let $N$ be the number of nonempty urns. Find $\text{Var}(N)$. Give an exact fraction.

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题目3206 · 概率

Variance of Trials to Reach 5 Successes

Independent Bernoulli trials succeed with probability $\frac{2}{5}$. Let $T$ be the first time the cumulative number of successes reaches 5. Use Wald-style second-moment reasoning to compute $\mathrm{Var}(T)$.

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题目5606 · 数理金融

Variance Risk Premium Arithmetic 1

A simplified volatility contract settles on annualized variance difference notional × (implied_vol^2 - realized_vol^2). If implied volatility was 0.26 and realized volatility turned out to be 0.19, what is the signed variance gap and the contract PnL on notional 2,000,000? Which

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题目4691 · 数理金融

Variance Shock Half-Life 1

A mean-reverting stochastic-vol model has mean-reversion speed kappa = 1.5. What is the half-life of a variance shock?

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题目5888 · 数理金融

Variance-Notional Swap Settlement

A variance swap is quoted with a variance notional of 5,000 per variance point (where a variance point is one unit of 100*sigma^2, i.e. payoff = VarNotional * (10000*sigma_realized^2 - 10000*K_vol^2)). The volatility strike is K_vol = 0.20 and realized annualized volatility over

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题目2117 · 数理金融

Variance-Swap Sampling Intuition 22

A quarter has only two very large overnight gap moves and otherwise tiny close-to-close returns. Why can realized variance still end up far above what a smooth diffusion intuition would suggest?

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题目2116 · 数理金融

Variance-Swap Surface Intuition 21

Two one-year equity option surfaces have the same ATM implied volatility, but Surface B has much more expensive downside puts than Surface A. Why can Surface B still imply a meaningfully higher fair variance-swap strike?

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题目367 · 概率

Variance of a Geometric-Stopped Exponential Sum

Let $N \sim \operatorname{Geometric}(1/2)$ (so $P(N = k) = (1/2)^k$ for $k = 1, 2, \ldots$) and, given $N$, let $X_1, \ldots, X_N$ be i.i.d.\ $\operatorname{Exp}(1)$. Set $S = X_1 + \cdots + X_N$. Using the law of total expectation and Eve's law, find $E[S]$ and $\operatorname{Va

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