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Problem 1 Consider a two-date economy where there are three states of the world at date 1. Consumption per capita at date 1 will be $5, $10, or $15. A security that pays one unit of consumption next period is worth $8 today. The risk-free security pays a gross return of 1.1. A call option on per capita consumption with an exercise price of $12 costs $1. The probabilities of the three states are 0.3, 0.4, and 0.3, respectively. a. Are markets complete? If yes, what are the state prices? b. Price a put option on per capita consumption with an exercise price of $8. с. Can you derive the risk-neutral probabilities?

Problem 1 Consider a two-date economy where there are three states of the world at date 1. Consumption per capita at date 1 will be $5, $10, or $15. A security that pays one unit of consumption next period is worth $8 today. The risk-free security pays a gross return of 1.1. A call option on per capita consumption with an exercise price of $12 costs $1. The probabilities of the three states are 0.3, 0.4, and 0.3, respectively. a. Are markets complete? If yes, what are the state prices? b. Price a put option on per capita consumption with an exercise price of $8. с. Can you derive the risk-neutral probabilities?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Problem 1 Consider a two-date economy where there are three states of the world at date 1. Consumption per capita at date 1 will be $5, $10, or $15. A security that pays one unit of consumption next period is worth $8 today. The risk-free security pays a gross return of 1.1. A call option on per capita consumption with an exercise price of $12 costs $1. The probabilities of the three states are 0.3, 0.4, and 0.3, respectively. а. Are markets complete? If yes, what are the state prices? b. Price a put option on per capita consumption with an exercise price of $8. с. Can you derive the risk-neutral probabilities?
Transcribed Image Text:Problem 1 Consider a two-date economy where there are three states of the world at date 1. Consumption per capita at date 1 will be $5, $10, or $15. A security that pays one unit of consumption next period is worth $8 today. The risk-free security pays a gross return of 1.1. A call option on per capita consumption with an exercise price of $12 costs $1. The probabilities of the three states are 0.3, 0.4, and 0.3, respectively. а. Are markets complete? If yes, what are the state prices? b. Price a put option on per capita consumption with an exercise price of $8. с. Can you derive the risk-neutral probabilities?
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