Dynamic Hedging of Mismatched Yen-Denominated Nikkei Puts
Summary
The document explains why a dealer issuing currency-protected Nikkei put warrants may need to trade the Nikkei as well as yen. The dealer’s assets were a varied set of yen-valued Nikkei puts, while its liabilities were a more homogeneous set of dollar-valued puts sold to clients. Differences in strikes, maturities, and currency exposure meant the positions did not offset each other exactly.
As the index and USD/JPY rate moved, the relative risk of the assets and liabilities changed. Dynamic trading in Nikkei futures, yen, and some individual Japanese stocks helped manage that changing mismatch. The cited account says the book was hedged at least daily and sometimes more often. The explanation addresses the misconception that a falling index would simply pass through as a matching gain for the dealer. It does not provide hedge ratios, pricing details, or a worked risk calculation, so it is a qualitative account of the hedging rationale.
Key ideas
- A dealer’s option assets and liabilities can differ in strike, maturity, and currency denomination.
- Changes in the index and exchange rate can alter the net risk even when both sides reference Nikkei puts.
- Dynamic index trading helps manage changes in the mismatch between the dealer’s option book and issued warrants.
- The cited account describes frequent hedging with futures, currency, and some individual stocks.
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Full text
# Kingdom of Denmark Nikkei put warrants # Kingdom of Denmark Nikkei put warrants 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! ## Answer by Alper (score 3) https://quant.stackexchange.com/a/73840 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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.