Following the successful first invitation, you have been invited again as a guest speaker to discuss the pricing of options and options trading. You consider examples of trading and pricing options on S&P 500 index futures and you also highlight the difference between historical and implied volatilities.

On December 1st, 2019, a client placed the following order on an online trading provider:

long 2 European March 2019 call index futures option contracts with strike 3150, and long 1 European March 2019 put index futures options contracts with strike 3150.

On December 1st, 2019, the S&P 500 is currently standing at 3146, the four-month futures price of the S&P 500 index is standing at 3149 and has a volatility of 15% per annum. The risk free interest rate is 3.10% per annum with continuous compounding. For the calculations, round-off the maturity of the March 2020 options to four months.

(a) Use the Black Scholes's model to estimate the premium involved to trade these options. Did the client pay or receive this premium?

We have already completed this question however we've included it for your reference

(b) Identify the strategy that the client used and provide the table and the diagram of the expected profit/loss generated by the strategy.

How do we calculate the payoff table and diagram? we cant work out the table as the numbers don't make sense.

(c) Discuss the profit and loss potential associated with this strategy. What was the client's expectation on market volatility and direction (bull or bear) when he placed the order?

Also included for reference.

(d) Calculate the profit/losses made if he exercises in March 2020 under two scenarios; the index futures price is 1) 3450 or 2) 2850. Discuss the strategy outcome.

How do we calculate this if we have no beta to calculate the rm. We also don't have the yield to calculate the rm.