# Suppose that aggregate time 1 consumption can only take on the values 1, 2, ... , K

## Question:

Suppose that aggregate time 1 consumption can only take on the values 1, 2, ... , K for some finite integer K. Assume that European call options on aggregate consumption are traded for any exercise price 0, 1, 2, ... , K. Consider a portfolio with one unit of the option with exercise price k − 1, one unit of the option with exercise price k + 1, and minus two units of the option with exercise price k. What is the payoff of this portfolio?

Discuss the consequences of your findings for the (effective) completeness of the market.

Could you do just as well with put options?

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