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A Three-Month At-The-Money Call Option on a Stock Index Is

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A three-month at-the-money call option on a stock index is trading at $5;the index is trading at $50.A forward start option on the index that comes to life in one month,has a life of three months from that point and that will be at-the-money when it comes to life,is trading at $4.98.The one-month rate of interest is 2% in continuously-compounded and annualized terms.What is the one-month forward price of the index?


Definitions:

Equilibrium

A state in which market supply and demand balance each other, and as a result, prices become stable.

MU/P Ratio

The ratio of marginal utility (MU) to price (P), used to determine the optimal consumption point where consumer satisfaction per unit of cost is maximized.

Marginal Utility

The heightened benefit received from using one more unit of a good or service.

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