On 12 August 2009 Bank of America (BAC) stock closed

On 12 August 2009 Bank of America (BAC) stock closed at $15.93. On the same date, a January 2010 call and a put on BAC with exercise price X = 16 traded at $2.25 and $2.37 respectively. 

Both options expire 15 January 2010. 

• Compute the implied volatility for each of the options. 

Assume that the annual, continuously-compounded, interest rate is r = 1.5% 

• How do the implied volatilities compare to the annualized historical volatility of BAC returns over the last 5 years? And the last year? 

• Assume that put-call parity holds and that the call is priced correctly. 

What should be the price of the put?