An at the money 3-month call option on the SPX index is currently trading at $52.82 on CBOE. An investor wishes to price a 3-month put option on the SPX. Suppose the SPX is currently at 1400, and the put is also at the money (i.e. currently the price of the index is exactly the same as the exercise price of the option written on this index.) Take the volatility of the return on SPX to be 15% and the risk-free rate to be 6%. Find the price of the this put option.