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Suppose you are long a TRYJPY call option. And lets say you can delta hedge using USDTRY, AUDJPY, and AUDUSD.

In this case I would delta hedge by buying USDTRY, selling AUDJPY, and buying AUDUSD.

If this were to be the case, I am creating correlation risk between these currency pairs?

Also, if we were to delta hedge using just USDTRY and USDJPY, would this eliminate the correlation risk?

This example is kind of odd to me as correlation risk is created without having any basket options on the book.

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yes you have introduced correlation risk since you have introduced spot positions in different currencies. but also, you could think about your original option position as having already had correlation risk , since the implied vol of the TRYJPY cross depends on the correl of USDTRY and USDJPY

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  • $\begingroup$ It would be helpful if you can spell out what you mean by "correlation risk" as it is possible that we are referring to different kind of correlation risk. When I think of correlation risk, I think of basket options. For instance, if I were to have a basket of two options which have negative correlation, I would be able to buy the basket cheaper. Based on your response, the correlation risk you are referring to seems to be on the underlying spot. $\endgroup$ – Byng Aug 15 at 18:18
  • $\begingroup$ Additionally, you mentioned that a TRYJPY option entails correlation risk because it has to be hedged by USDTRY and USDJPY. If so, does this mean that EURJPY, which is also a direct pair, has correlation risk because it can be hedged using EURUSD and USDJPY? $\endgroup$ – Byng Aug 15 at 18:20
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    $\begingroup$ the implied vol of the TRYJPY cross depends on the correl of USDTRY and USDJPY because: totvol(TRYJPY) = stdev(ln(TRYJPY)) . var(lnTRYJPY) = var(ln(A) + ln(B)) = totvolsq(A) + totvolsq(B) + 2*correl*totvol(A)*totvol(B) , where A=TRYUSD, B=USDJPY. $\endgroup$ – Randor Aug 27 at 12:23
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The cross currency basis of the 3 pairs of hedging positioning are the sources of unhedged risks. The currency hedging demand in AUD, TRY and JPY will drive some Pnl in the book. Not sure if this is the only source of correlation risk here.

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  • $\begingroup$ Obviously the maturity date and the settlement date is some time in the future, but delta hedging is done via spot, not forwards. In this regard, can you elaborate what you mean by the xccy basis of 3 pairs and where this "unhedged" risk might be introduced? $\endgroup$ – Byng Aug 15 at 18:05
  • $\begingroup$ I was assuming hedging with forwards. If hedging with spot, what FX cash do you hold assuming your home currency is USD? $\endgroup$ – hotsource Aug 16 at 22:00

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