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

1. Find the price of the put option, using put call parity

2. Find the price of the put option using Black Sholes option pricing formula for puts