Piecewise Linear-Payout on Hang Seng Index
Once again the investor is bullish on the Hang Seng index (Hong Kong equities), however, he wants a pay-off in a more controlled manner and such that his pay-off increases with the increase in the index.
The current level of Hang Seng index is 12,393 and the historical volatility is assumed to be 17.74%. For a notional USD amount of 1 million the investor buys an instrument that has the following pay-offs:
|At 12,393 or below this level
||Pay-off = 0
|Between 12,393 to 13,000
||Pay-off = $1 million * ($1 for every 10 point increase in the index)
|Between 13,001 to 14,000
||Pay-off = $1 million * ($2 for every 10 point increase in the index)
|For 14,001 and above
||Pay-off = $1 million * ($5 for every 10 point increase in the index)
The above is a linear pay-out function. The pay-out can be replicated by buying and selling a finite number of calls at the strike prices 12,393, 13,000 and 14,000.
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