You know the current value of a call option on the S&P500 with a strike price of 2300 and one-year maturity is $176. The S&P500 is currently trading for 2313.50, and it is expected to pay a 2% annual dividend yield over the next few years. The current term structure of riskless interest rates is flat at 5%.

Recall the binomial formula C = SN(x) - Ke^-rtN(x - sqrt(t)).

(a) What is the implied volatility of the call option?

(b) Using the Black-Sholes model, what would you estimate as the value of a put with a strike of 2300 and one year maturity on the S&P500 to be?