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I have read in a book from Emanuel Derman that Goldman Sachs manufactured a derivative in the early 90's that consisted of buying cheap puts on the Nikkei index (and paid in Yen) and combining them which a Yen-USD protection and resold them to clients. This construction was called the "Kingdom of Denmark" puts.

To hedge this construction, they must dynamically trade Yen-USD and also the Nikkei index. Can someone explain to me why you also want to trade dynamically the Nikkei index if you want to hedge the whole construction?

I thought that if the Nikkei drops, then Goldman gets paid and forwards the money to its clients. So, there is no need for Goldman to protect itself against the decreases in the Nikkei index.

Any comments or thoughts are welcome!

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  • $\begingroup$ Intuitively, because of non-zero correlation between Nikkei and USDJPY Goldman did have some exposure to Nikkei, which it had to hedge. See later pages in the book where he discusses correlation, Karasinski's formula, etc. $\endgroup$
    – Alex C
    Sep 8, 2019 at 15:11
  • $\begingroup$ @AlexC, I hope I have understood the book correctly: Let's assume that the Nikkei index and the Yen are positively correlated. If the Nikkei index had plunged the Yen would have depreciated against USD. Hence, Goldman would have wanted to be short in the Nikkei index to hedge its position. But this in turn requires another USD-Yen hedge as being short in Nikkei means receiving Yen. Is this correct? $\endgroup$
    – Philipp
    Sep 8, 2019 at 15:58
  • $\begingroup$ That is what I think. I hope someone else here can confirm that, and put in mathematical terms... $\endgroup$
    – Alex C
    Sep 8, 2019 at 16:27

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I assume you are referring to the sentence in italics (italicization belongs to me) in the following paragraph on pp. 218-219 in Derman's book "My Life as a Quant".

Though no one used that term in those days, it was Piotr [Karasinski]’s “financial engineering” that showed us how to eliminate the mismatch between the risk of the warrants we owned and the GER puts we sold. Executing the hedge in practice was more complicated. The trading desk was long a diverse assortment of yen-valued Nikkei puts. They were correspondingly short a large homogeneous batch of the dollar-valued Kingdom of Denmark Nikkei puts that Goldman had issued. To hedge the mismatch, they had to continually trade varying quantities of Nikkei futures and yen currency, as well as some individual Japanese stocks. This entire “Nikkei book” had to be hedged at least once each day, and sometimes more often.

As stated in the quote, the Nikkei puts Goldman had at the time among its assets not only had different characteristics (strike price, maturity, etc.) than those it was selling but also from each other.

That means, the Nikkei puts in Goldman's assets had varyingly different risk profiles than those in its liabilities; as the Nikkei index and the USD/JPY exchange rate changed, the differences in the risk profiles of the puts in assets and liabilities have changed, requiring Goldman to take action frequently to keep them balanced against each other.

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