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Options on total return indices
If one wants to price an option on a total return index, such as S&P 500 total return, and use Black Scholes, is it sufficient to set the dividend yield on the index to zero? If not, what should be used? Are the other inputs to the formula the same as if the underlying was the S&P 500 price index?Thank you.
Options on total return indices
QuoteOriginally posted by: UnowenIf one wants to price an option on a total return index, such as S&P 500 total return, and use Black Scholes, is it sufficient to set the dividend yield on the index to zero? If not, what should be used? Are the other inputs to the formula the same as if the underlying was the S&P 500 price index?Thank you.Yes if dividends are reinvestedk, then the drift becomes r (under risk-neutral assumptions) and you can just set q to 0.
Options on total return indices
you might also want to consider the fact the volatility of the total return index will be smaller than that of the price return index.
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- Yossarian22
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Options on total return indices
QuoteOriginally posted by: daveangelyou might also want to consider the fact the volatility of the total return index will be smaller than that of the price return index.this is not true if you are speaking about implieds.
Options on total return indices
I really could not get the mathematics on why volatility of total return will be smaller. Can somebody help me to get better understanding?
Options on total return indices
Could it be that dividend streams are stable, and adding a stable cashflow to a volatile cashflow reduces that volatility. But if the dividend yield is low and the options are not very liquid then the volatility of the total return could well be higher than the price index.
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- Yossarian22
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Options on total return indices
for TR relative to strike-equivalent PR vol has moved from negative to positive. the Market never lies.In theory the volatility should be lower since you are not exposed to div yield risk. Remember variance is additive so no div volatility => lower TR vol. It should be lower because of less gamma.