Consider the following 5 year product on the S&P 500 Index: Notional: $1,000,000
ID: 2758058 • Letter: C
Question
Consider the following 5 year product on the S&P 500 Index: Notional: $1,000,000. Maturity: 5 years. Underlying Index: S&P 500 (SPX).
Payoff: Notional x min (1.2 x SPX final / SPX initial, 1.5), where SPX final is the level of the S&P 500 index on the maturity date, and SPX initial =1900 is its level on the issue date.
Draw the payoff on this product as a function of SPX final.
How does this product compare with a direct investment in the S&P 500 index?
Find the arbitrage price of this product using the following market data:
SPX Spot
1900
Strike
5-year European Call
5-year European Put
0
1628.70
0
1900
249.001
346.6295
2100
154.3132
446.2875
2375
61.5418
620.7418
2600
32.8290
810.6682
SPX Spot
1900
Strike
5-year European Call
5-year European Put
0
1628.70
0
1900
249.001
346.6295
2100
154.3132
446.2875
2375
61.5418
620.7418
2600
32.8290
810.6682
Explanation / Answer
Payoff for this product can be split into two parts.
The payoff will be a straight line with an increment of $ 631.58 for each unit increase in SPX final from 0 to 2375.
Increment calculation = 1.2 x 1 / 1900 x 1,000,000 = $ 631.58
Breakeven strike point calculation for SPX final = 1.5 x 1900/1.2 = 2375
Beyond 2375, the value of the payoff is a straight line of 1,500,000.00
The payoff of the above product looks like that of a vanilla sell put option compared to a direct investment in S&P 500 index which will be a straight line (Options vs Futures)
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