Question
Data: Assume the following hypothetical values: Starting value for SPY ETF: 390; Dividend yield: 1.65% (contin. compounded, annualized rate); risk-free interest rate over the life
Data: Assume the following hypothetical values: Starting value for SPY ETF: 390; Dividend yield: 1.65% (contin. compounded, annualized rate); risk-free interest rate over the life of the option: 3.80% (contin. compounded, annualized rate). Assume that 75-day European-style call and put options on the SPY can be bought or written at any desired strike price, with the Black-Scholes-Merton model providing the fair value for the options. Assume that the implied volatility of the index for pricing the options is a 24% 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 75 days and depend upon the terminal value of the SPY in 75 days from now. Assume that the options and SPY ETF can be transacted in any integer amount (so not restricted by option-contract convention), and that the ELS has a scaling of 100 times the SPY price (which means the scaling would be 100 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 SPY ends up at 390 in 75 days, then the ELS pays off at 390 per unit at expiration (or $39,000 with the 100 multiplier).
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. 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.
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