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中文题目
题目5654 · 数理金融

Asian Path Payoff 4

A simulated path for an arithmetic-average Asian call is [95, 92, 90, 97] with strike 94. What payoff does this single path contribute to the Monte Carlo estimator?

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题目2910 · 概率

Simple Walk on a Three-State Path

Consider the path graph $1\leftrightarrow 2\leftrightarrow 3$. A simple random walk moves to a uniformly chosen neighbor. Find the stationary distribution.

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题目3881 · 金融与交易

Why a Zero-Net Path Still Matters 1

A long futures account uses multiplier 200 and starts each scenario with margin 7000. Path A settlements are [100, 95, 92, 100] and path B settlements are [100, 98, 96, 100]. Maintenance margin is 5600. Treasury restores the account to the initial margin after any margin call. Wh

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题目3882 · 金融与交易

Why a Zero-Net Path Still Matters 2

A short futures account uses multiplier 220 and starts each scenario with margin 8000. Path A settlements are [70, 75, 77, 70] and path B settlements are [70, 72, 74, 70]. Maintenance margin is 6500. Treasury restores the account to the initial margin after any margin call. Which

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题目3884 · 金融与交易

Why a Zero-Net Path Still Matters 4

A long futures account uses multiplier 100 and starts each scenario with margin 5000. Path A settlements are [40, 46, 41, 45] and path B settlements are [40, 42, 43, 45]. Treasury sweeps any balance above the initial margin back to cash after each close, and maintenance never bin

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题目3885 · 金融与交易

Why a Zero-Net Path Still Matters 5

A short futures account uses multiplier 100 and starts each scenario with margin 6000. Path A settlements are [80, 74, 79, 75] and path B settlements are [80, 78, 77, 75]. Treasury sweeps any balance above the initial margin back to cash after each close, and maintenance never bi

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题目2737 · 脑筋急转弯

Inventory Paths With Holds Inserted

A trader executes 4 buys, 4 sells, and 2 holds. Buys and sells each change inventory by plus or minus 1, holds leave inventory unchanged. The trader starts flat, ends flat, and inventory may never become negative at any intermediate time. How many execution sequences are possible

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题目548 · 概率

Commute Time Between Endpoints of a Path

Consider the path graph $P_n$ with vertices $\{0, 1, \ldots, n-1\}$ and $n-1$ edges (each of unit resistance), where the walk at interior vertices moves left or right with equal probability, and at the endpoints moves to the unique neighbor. (a) Compute the effective resistance

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题目531 · 概率

Cover Time of the Path Graph P₃

A random walk moves on the path graph $P_3$ with vertices $\{1, 2, 3\}$ and edges $\{1{-}2, 2{-}3\}$. At each step, the walker moves to a uniformly random neighbor (so from vertex $2$ it goes to $1$ or $3$ each with probability $\tfrac{1}{2}$, and from vertex $1$ or $3$ it moves

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题目546 · 概率

Hitting Time on the Path Graph P₅

A simple random walk moves on the path graph $P_5$ with vertices $\{0,1,2,3,4\}$ and edges connecting consecutive vertices. At the interior vertices ($1, 2, 3$), the walker moves left or right with equal probability $\tfrac{1}{2}$. At the endpoints ($0$ and $4$), the walker moves

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题目5656 · 数理金融

Required Path Count 1

A pricing engine estimates that the discounted payoff standard deviation is about 6. How many Monte Carlo paths are needed to drive the standard error down to at most 0.15?

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题目5657 · 数理金融

Required Path Count 2

A pricing engine estimates that the discounted payoff standard deviation is about 3.5. How many Monte Carlo paths are needed to drive the standard error down to at most 0.08?

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题目5872 · 数理金融

Realized Vol From A Six-Day Path

Over six days the daily returns were [0.010, -0.015, 0.022, -0.006, 0.013, -0.009]. Using realized vol = sqrt(252 × average(r^2)), what annualized realized volatility results (four decimals), and was it above or below a quoted 20% implied?

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