This is a question related to OPTIONS, a DERIVATIVE in finance.

The following questions are related to a short strange strategy for stock SPY.

Current Price as of today: 456.40

Historical volatility of returns: Daily volatility is 0.000997915 and annual is 6.28628E-05

The short strangle will involve selling a short put with a Strike price of $460 with an expiration date April 19th and selling a short call with a strike price of $465 also expiring on April 19.

Both these options are on the money.

Premium from short call = 15.7

Premium from short put = 4.27

This is the payoff table.

Part 1:

1. Using prices of options, calculate the cost of the strategy.
2. Find the breakeven points for the strategy. This means that you need to calculate the prices of the underlying stock, at which your strategy results in zero profit/loss.
3. Find the maximum profit for your strategy and indicate the range of prices at which you can earn this maximum profit.
4. Find the maximum loss for your strategy and indicate the range of prices at which the strategy will experience the maximum loss.
5. Construct the profit/loss graph for your strategy.

Part 2:

1. Use the Black Scholes Option Pricing model to calculate prices of your options, using historical volatility.
2. Compare the market prices of your options from above to those obtained by using the Black Scholes Option Pricing Formula.

\begin{tabular}{|c|c|c|c|} \hline & S=465 \\ \hline Short Put on 460 & s460 & 0 & \\ \hline Short Call on 465 & 0 & 0 & s465 \\ \hline Total & s460 & 0 & s465 \\ \hline \end{tabular}