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ellerton
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Joined: February 19th, 2005, 2:55 pm

Index Yield for Pricing/Analysing Index Options

February 22nd, 2005, 6:21 pm

I am trying to perform analytics on any Index Option.I currently use the ATM options to generate a theoretical future value and then calculate the index dividend yield from this. The problem here is that the calculated yield fluctuates widely throughout the day. (eg. Current yield for the FTSE 100, 18thMarch is approximately 12% but the value generated from the options has a daily range of about 11.25 to 12.25%). I see two possibilities:1/. Use some form of averaging throughout the day.2/. Calculate the index dividend yield based on discrete dividend cash flows of the individual constituents. This can be calculated using the historical dividend payments and consensus estimates and then assuming that the same pattern will continue.Which method would be most appropriate to use?
Last edited by ellerton on February 22nd, 2005, 11:00 pm, edited 1 time in total.
 
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erstwhile
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Joined: March 3rd, 2003, 3:18 pm

Index Yield for Pricing/Analysing Index Options

February 23rd, 2005, 2:13 pm

One problem i can see is that you have quite a short dated contract (less than one month to expiry).A range of 1% anualised dividend yield would be around 8bp dividends for a month which amounts to about 4 index points on the forward.For a 50 delta option this would mean a variation of 2 index points on the option quotes.Looking at the ATM options right now I see a bid-ask spread of 1.5 index points on both calls and puts, so much of the noise you are getting is just bid-ask pricing.What might be better is to use the march futures contract on the FTSE, as there is very unlikely to ever be any riskless arbitrage of the put-call against future variety.I think you wil get far more stable results.
 
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ellerton
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Joined: February 19th, 2005, 2:55 pm

Index Yield for Pricing/Analysing Index Options

February 24th, 2005, 12:35 pm

Thanks Erstwhile.I have experimented using both the ATM options and the Futures and generally found that the range on the value generated from the futures is approximately 10% wider with a similar mean. (see attached .xls file). With the options I basically use the methodology in the VIX White Paper [http://www.cboe.com/Institutional/RCInstitutional.aspx]. The other issue with using the future is that there are more Option Expiries than Futures Expiries so I would have to derive a theoretical futures price anyway.I have also noticed that when using future dividend yields (even if many of the values are actual announced dividends) to generate the short term yield (eg. March) the values I get consistently understate the implied yield generated from the futures/options. In a few cases (1 in the case of the CAC) the forecast dividends are missing but this is for either a low dividend paying or low weighted stock. Is there theoretical reason for this?(eg. For the CAC 40 at 13.40pm CET I have an implied yield for 18th March of 0.356% and 20th of May of 5.190%; the same result based on the discrete cash flows of the underlying (see attached .xls) is 0.00% and 4.42%. Maybe the forward looking data I am using is bad.
 
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erstwhile
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Joined: March 3rd, 2003, 3:18 pm

Index Yield for Pricing/Analysing Index Options

February 24th, 2005, 1:44 pm

methodology looks ok - hmmm...maybe something to do with settlement date on the option contract? maybe the daycount for discounting is different from the daycount for volatility? or maybe the quotes you had came off the "autoquote system" which may have an interest rate that is a bit off from the rate used by cash-futures arbitrageurs?is there any issue with continuous rates and yields vs market quoted rates?
 
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ellerton
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Index Yield for Pricing/Analysing Index Options

February 24th, 2005, 2:00 pm

Will convert market rates to continuous and retry. . .
 
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ellerton
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Index Yield for Pricing/Analysing Index Options

February 24th, 2005, 2:02 pm

They are the regular quotes and not the Auto quotes.The settlements for the March expiry match.
 
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erstwhile
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Index Yield for Pricing/Analysing Index Options

February 24th, 2005, 2:30 pm

here's a thought - if you use two sets of calls and puts, you can make a finance box and calculate the interest rate being used by the market.you do this (K1 is the high strike):Call(K2)-Put(K2) - [ Call(K1) - Put(K1) ] = (K2 - K1) * exp( - R*T)and solve for R to get the rate implied by the forwardsif i do this for your FTSE data and average over all the discount factors i get an implied continuous rate of 4.15%, which is quite a bit different from the 4.97% you have in the spreadsheet.so the option prices themselves are implying an interest rate that disagrees with your assumption. i would follow this lead.