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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:

Variable Overhead

Costs of overhead that vary with the level of production activity, such as utilities for machinery or materials handling expenses.

Predetermined Overhead Rate

An estimated rate used to allocate manufacturing overhead costs to individual units of production based on a certain activity base.

Variable Component

The part of a cost or expense that varies directly with the level of activity or production volume, in contrast to fixed costs.

Electrical Motor

An electromechanical device that converts electrical energy into mechanical energy, commonly used in various appliances, machinery, and vehicles.

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