7. Assume that the true formula for pricing options is unknown, e.g., Black-Scholes is not...

7. Assume that the true formula for pricing options is unknown, e.g., Black-Scholes is not applicable. Hence, you are asked to use the following approximation for the insurance value of a put option:

where S is the current price of the stock, K is the strike price, σ is the volatility of the stock return, and T is option maturity.

You are given that S = 100, K = 105, and the interest rate r = 1%. Option maturity is T = 1 year, and there are no dividends.

What is the maximum volatility for which early exercise of the option is induced?