Consider a Binomial Tree in Which the Stock Moves Up $2 i$

question 7

Multiple Choice

Consider a binomial tree in which the stock moves up by a factor $2 i$ and down by a factor $d$ , respectively with probabilities $p$ and $1 - p$ . The variance of log-returns per time step is given by the following formula:

• A) \(p ( 1 - p ) [ \ln ( u d ) ] ^ { 2 }\)
• B) \(p ( \ln u ) ^ { 2 } + ( 1 - p ) ( \ln d ) ^ { 2 }\)
• C) \([ p \ln u + ( 1 - p ) \ln d ] ^ { 2 }\)
• D) \(p ( 1 - p ) ( u / d ) ^ { 2 }\)

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Definitions:

Semiarid Zones

Regions characterized by light rainfall, usually between 10 and 20 inches per year, often resulting in scanty vegetation and a steppe climate.

Terrestrial Biomes

are large community units, distinguished by their predominant vegetation and are adapted to specific climate conditions on Earth, such as forests, deserts, and grasslands.

Alpine Tundra

A biome found in the high mountain regions of the world, above the tree line, characterized by windswept landscapes, low temperatures, and minimal vegetation.