Use the Greek calculator spreadsheet (Option type: Black-Scholes European) for this problem. You will also need market data on SPY and its options, found in the following links:

https://finance.yahoo.com/quote/SPY?p=SPY

https://finance.yahoo.com/quote/SPY/options?p=SPY

You are considering a position that consists of European at-the-money call and at-the-month put options[1], with an expiration date of the third Friday of the next closest month. (If it is September now, the option expires in the third Friday of October). Assume the standard deviation of SPY is 20% over the next month. Risk-free rate is 1%, and SPY dividend yield is 1.5%.

a)Compute a fair price for the call and put options and the associated Greeks.

b)We buy 100 of the ATM put. We need add to 100 ATM calls to create the straddle position. What should the weights for the ATM call be so that the resulting portfolio is delta-neutral? This is known as a delta-neutral straddle position. By how much will the value of the delta-neutral straddle position change if the SPY's standard deviation increase from 20% to 22%?