Final answer:
To calculate the implied volatility, an iterative numerical method must be used to adjust the volatility value in the Black-Scholes model until the theoretical option price matches the given market price ($8.50). Direct calculation cannot be provided here due to the need for computational tools.
Step-by-step explanation:
The student's question pertains to the concept of implied volatility in the context of option pricing using the Black-Scholes model. To calculate the implied volatility, we need to run an iterative process, initially using the given volatility and adjusting it until the theoretical price generated by the Black-Scholes formula matches the market price of the option.
However, since the actual calculation of implied volatility requires a numerical method such as the Newton-Raphson method, which cannot be performed here without computational tools, we can only define the process. The implied volatility is the volatility value that, when input into the Black-Scholes model, will return the current market price of the option, which is $8.50 in this case.
This calculation carries importance in financial markets as it reflects the market's expectation of the stock's volatility over the life of the option. It cannot be computed directly from the question's information without computational resources or software designed for this purpose.