Final answer:
The question concerns the pricing of an American-style index put option with specific parameters. To compute a price, models like the binomial option pricing model are used. Early exercise of such options is generally not advantageous since indices do not pay dividends.
Step-by-step explanation:
The question relates to the pricing of an American-style index put option with a strike price of 7000, an underlying stock index at 6900, a volatility of 40%, and a risk-free rate of 4.5%. Computing the price using one-month steps typically involves using a numerical method such as the binomial option pricing model or a similar lattice approach, but the complexity of this calculation goes beyond a simple explanation or generic answer format.
Moreover, as the underlying asset is an index and the option is American-style (which allows for early exercise), early exercise may be advantageous if the option is deeply in the money interest rates are sufficiently high or underlying dividends are expected. However, because indices do not typically pay dividends, early exercise for an index put option is less likely unless it compensates for the risk-free interest rate that could be earned if the proceeds from exercise were invested at the risk-free rate.
It's important to note that the provided reference information discussing interest rates and bond pricing does not directly pertain to the calculation of an option's price, although it does demonstrate the principle of discounted cash flows, which is a fundamental concept in option pricing.