Data:

Hypothetical starting value for S&P 500 index: 3920; Dividend yield: 1.50% (contin. compounded, annualized rate); risk-free interest rate over the life of the option: 0.10% (contin. compounded, annualized rate). Assume that 3-month European-style call and put options on the S&P 500 index can be bought or written at any desired strike price, where the Black-Scholes-Merton model provides the fair value for the options. Assume that the implied volatility of the index for pricing the options is a 21% annualized standard deviation. Ignore any considerations of margin requirements for the derivative contracts.

Consider the following possible ELS. The terminal cash flows for the ELS would occur in 3 months and depend upon the terminal value of the S&P 500 index in 3 months from now. Assume that the options and SPY ETF can be transacted in any integer amount, and that the ELS has a scaling of 100 times the S&P 500 price (which means the scaling would be 1000 SPY units).

You will need to figure out the underlying holdings and price to offer the following ELS:

ELS Payoff Description:

-For no price movement:

1) If the S&P 500 ends up at 3920 in 3 months, then the ELS pays off at 3920 per unit at expiration (or $392,000 with the 100 multiplier).

-On the Downside:

2) On the downside, for the first 12% decline in the S&P 500, the ELS would lose proportionally on a 0.5 to 1 basis (half as much loss on a per unit basis, as the S&P 500). So, if the S&P 500 price ended up at 3449.6 in 3 months, then the ELS payoff would be $368,480 at expiration. 3) For index price declines of more than 12%, then the ELS payoff would not fall any more. So, for example, if the S&P 500 ended up at 3000, the ELS payoff would still be $368,480 at expiration.

-On the Upside

4) On the upside up to an S&P 500 increase of 5%, the ELS will payoff $2 more for every $1 increase in the S&P 500. (Or, a 2X payoff for S&P 500 increases between 3920 and 4116). So, if the S&P 500 ended up at 4116 in 3 months, the ELS payoff would be $431,200 at expiration. 5) For price increases in the S&P 500 between 5% but less than 15%, the ELS payoff does not increase any further, incrementally. So, for example, if the S&P 500 ends up at 4508 in 3 months, then the ELS payoff is still $431,200 at expiration. 6) If the S&P 500 price goes up by more than 15%, the ELS payoff increases on a 1 to 1 basis. So, for example, if the S&P 500 ends up at 4704 in 3 months, then the ELS payoff is $450,800 at expiration.

To make sure that you understand the ELS Payoffs, below is a graph of the PAYOFFS at ELS EXPIRATION only, over a range of possible terminal S&P 500 prices in 3 months from now. Note that this is NOT THE SAME as the Profit, because the Profit is the Payoff minus the Initial Cost of the ELS.

For this ELS:

A. If you are the issuer of this ELS, what should be your holdings of options and the SPY ETF to generate the future cash flows for the above ELS? (Remember that a share of the SPY ETF is scaled at 1/10 of the S&P 500, so you will need 1000 SPY as the equivalent of 100 S&P 500 units) For simplicity, assume that the issuer keeps the dividends from the underlying index over the life of the contract as the spread, so that the ELS can be offered at a price based on the current fair values of the options and ETF.

B. What do you estimate as an initial market price for the ELS above, given the assumptions in A. above and assuming that we can use the Black-Scholes-Merton model to value the options? (Round all individual option prices from the spreadsheet to the penny, $0.01, in your downstream calculations). Paste in a copy of the input cells and output price from the BlackScholes-Binomial option pricing spreadsheet for one of the options as an appendix in your report, so I can check that your inputs into the spreadsheet are correct.

C. Provide a graph using the Option Strategy Analyzer spreadsheet that shows the profit from buying the ELS at your initial price in B, over a range of possible terminal S&P 500 index values from 3,332 to 4,704, if the position is held to maturity. What is the breakeven terminal S&P 500 value for this ELS investment, assuming that the ELS is initially priced as in B. above? What is the profit in dollars and the corresponding percentage return if the S&P 500 went up 18%, based on the initial price in B. above? Include a copy of this Option Strategy Analyzer Excel spreadsheet that contains your profit graph as a separate file for your deliverables for this assignment.

Please answer A, B, and C thank you!