Quanto equity products depend on the correlation between the underlying and the fx rate between the underlying currency and the quanto currency.The traded implied correlations seem to deviate strongly from the historical correlations. E.g. for Nikkei quanto EUR, the correlation between EUR/JPY=0.007... and the Nikkei is traded at -0.15 but historical time series correlation is +0.20.What is the reason for this large markup?Does it even make sense to look at historical underlying/fx-correlation?Any hints are appreciatedpschwen

Is the market is pricing the correlation wrong? Or is the "correlation" right and you've set your Black-Scholes volatilities "wrong?" Or is the market trying to charge for a "forward looking" correlation?

Usually the market is pretty much one way on these. IBs sell quanto structures through to retail and so its tricky to find anyone with opposing position. When there is a one way market then this skews the marks.

our impression is that this "skew" seems to be a special feature of the Nikkei quantoed into EUR and USD. For other underlyings, e.g. STOXX50E quanto USD, we don't see such a large spread between implied and historical correlation.

A quick question - how are you backing out the market implied correlation? If you have asked a broker/IB for a quote for a particular quanto structure and you are using this together with the implied vol seen on screens for vanilla trades then might this lead to an inaccurate correlation? Presumably the broker/IB would charge a higher margin for this trade as it is less liquid, this will distort the premium that is quoted so you should not just use it without adjustment to derive an implied correlation.

QuoteOriginally posted by: RedAlertA quick question - how are you backing out the market implied correlation? If you have asked a broker/IB for a quote for a particular quanto structure and you are using this together with the implied vol seen on screens for vanilla trades then might this lead to an inaccurate correlation? Presumably the broker/IB would charge a higher margin for this trade as it is less liquid, this will distort the premium that is quoted so you should not just use it without adjustment to derive an implied correlation.In the case of N225 quanto, it is extremely easy to back out the implied correlations, since N225 options (in Yen) and FX options on the USD and EUR crosses are all extremely liquid, so the only parameter you are left to back out in your Black model is the correlation. Better yet, there is also an active broker market that regularly quotes synthetic forward trades, such as long call+short put in yen traded together with short call+long put quanto EUR, so that you can trade the quanto forwards directly.As with volatility, historicals don't matter; all that matters is where the market participants choose to bid and offer correlation and other parameters. If you believe the negative implieds are wrong and the correlation will be positive in the future (based on what you've seen historically), by all means load up on long correlation positions

Hi pschwen,Not sure how important it might be but are you using FX spot vs Equity spot or FX forward vs Equity forward to get the correlation?If you look at the currency adjusted indicies from either side of the pond they are fairly well matched. As currency strengthens the index weakens. It seems easier for investors to compare US vs European companies on a like for like basis and hence will weight portfolios on currency adjusted prices. Eg GAP in USD vs H&M in EUR.With regards to Japan it may be tricky to compare like with like. How much do Muji's sales depend on US / Europe? Also on a currency adjusted basis the Nikkei is independent from Europe and US indicies. Japan has been following its own cycle over the last 15 years or so. Would this lack of industry comparisons and nature of Japan's comparative economic cycle make indicies fairly independent of FX rate?As there is less symmetry could this lead to one way market behaviour?Pabo

@pabo:Quoteare you using FX spot vs Equity spot or FX forward vs Equity forward to get the correlation?are you asking about the way we computed historical correlation?We used daily spot fx rates and .N225 closing time series and computed the correlation of the series of log returns.A possible problem could be the time sync of the sampled time series, so we tried different fx fixings - NY, London and Tokio for the fx rate, but the net effect on correlation was only little.We also looked at the width of the correlation distribution sampled by bootstrapping in a given time window, but this width was well below the spread between historical and implied. Same effect from varying time windows. So our impression is that the historical correlation estimation is quite stable and the observed spread is a real market feature. @exotiq:Quoteif you believe the negative implieds are wrong and the correlation will be positive in the future (based on what you've seen historically), by all means load up on long correlation positions this trade idea is heavily based on the assumptions of the model, i.e. two linearly correlated GBM processes for the returns, isn't it? Best regardspschwen

Hi Pabo,Quoteare you using FX spot vs Equity spot or FX forward vs Equity forward to get the correlation?why do you think the FX forward and Equity Forward times series would be a reasonable choice for the computation of correlation?Best Regardspschwen

Whilst I totally agree with what exotique said, I just thought I would put in my 2 cents worth on calculating the correlation of asynchronous time series.Try using weekly data instead of daily data. With higher frequency data, a larger percentage of the total covariance will be made up of non-overlapping time periods. With weekly data, you will still have the same amount of nonoverlapping data, but as a percentage of the total co-movement of the underlyings it is much less.I first saw this when a colleague was pricing the infamous FTSE-S&P worst-of-2 put spread. If you use daily closing prices, correlation was around 30%. If you used weekly data is was more like 70%! Of course this is more likely to happen with equity index correlation than with an equity index against a currenty pair. But it might be worth having a look. By the way, I suggest using non-overlapping time periods. Do the calc for Monday data, Tuesday data, etc. If you find a wide variation by day of the week this should tell you something about the stability of the correlation figure you produce.For very long dated options (like 10yrs +) it may be important to look at the correlation of the historical forwards, but I expect for short dated options it wouldn't matter.Again pricing has almost nothing to do with historical data anyway, as exotique said.

Thanks a lot for all comments!