Analysis: extracting, aggregating and enriching the option Greeks

In the first part of this article, we will look at risk aggregation aspects.

Aggregating Delta, Gamma and Vega not only allows to risk manage a portfolio efficiently (which by itself is a piece of Business Intelligence) but it also provides alternative data insights.

To begin our analysis, we will focus on a specific stock—Nvidia—as our case study (the underlying).

Regarding the Greeks-extraction task, that’s the beginning of the valorization process, we chose as a first product a Barrier Reverse Convertible on NVIDIA:

As a first step, we need to extract the Greeks (Delta, Gamma, and Vega) for the structured product's embedded option—an exotic short down-and-in put option, from the investor's perspective—at the individual share level. The volatility is unknown, while the risk-free rate equivalent, for example, can be (rather) easily derived from the very high-quality yield curve.

The option’s parameters on the 5^th of May 2025 are: Stock price (end of day): 113.82 USD, Strike: 101.89 USD, Barrier: 56.05 USD, Expiration: 4 months, Risk-free: 4.35% (estimated), Volatility: 40.32% (estimated). Dividends are ignored.

The table below shows the Greeks for one share: our own valuation

Instrument (about)	Value	Delta	Gamma	Vega
Short down-and-in put	0.1243	0.0153	-0.0019	-0.0324

In the second step, we take into account the issue size of the structured product: the issue size is 11.8793 million USD, therefore the total number of shares involved is the number of shares per 1’000 USD (that is 9.81451) * issuing size in millions * (1’000’000 / 1’000) = 116’589.5086.

The above table is updated as follows for all the shares involved: simply multiply each value by the total number of shares.

Instrument total (about)	Value total	Delta total	Gamma total	Vega total
Short down-and-in put	14,492.08	1,783.82	-221.52	-3,777.50

Therefore, if the underlying stock price increases by 1 USD, the total change in the value of the option for all investors holding the structured product is approximately equal to the Delta Total multiplied by 1 USD, resulting in a change of about 1’783.82 USD.

Now, as the second product for the aggregation, we will consider a capital protected note on NVIDIA:

It includes a long call spread option combination with the following parameters on 5 May 2025: Stock price (end of day): 113.82 USD, Low Strike: 147.01 USD, High Strike: 214.6346 USD, Expiration: 2 years and 6.5 months, Risk-free: 3.85% (interpolated between the two- and three-years US Treasury rates, estimated), Volatility: 38% (estimated; we assumed the same volatility for both call options, although this is unlikely since their Strikes are quite different). Dividend yield: 0.028% (estimated).

The table below shows the Greeks for one share: our own valuation

Instrument (about)	Value	Delta	Gamma	Vega
Long call spread	20.5908 (Long call low strike) -9.0198 (Short call high strike) =11.5710	0.515939 - 0.279484 = 0.2365	0.005777 - 0.004876 = 0.0009	0.722796 - 0.610062 = 0.1127

The above table becomes as follows, for all the shares involved: one just multiplies by the total number of shares involved, in that case, it is the number of shares per 1’000 USD of 6.802258 * issuing size of 32.824 million * (1’000’000 / 1’000) = 223’277.3166.

Instrument total (about)	Value total	Delta total	Gamma total	Vega total
Long call spread	2,583,541.83	52,805.09	200.9496	25,163.35

Now, from an overall Risk Management perspective, it is important to consider the Greeks at the aggregate level, including all products: we therefore just add the Delta, Gamma and Vega values given at the “Instrument Total” levels. The Greeks are additive (when considering the same underlying), which is why the calculation is so straightforward.

The next table shows it in detail:

All structured products aggregated (about)	Delta aggregated	Gamma aggregated	Vega aggregated
Down-and-in short put AND long call spread	1,783.8195 + 52,805.0854 = 54,588.9049	-221.5201 + 200.9496 = -20.5705	-3,777.5001 + 25,163.3536 = 21,385.8535

That means that at the level of the two aggregated Structured Products (of course, there are many more NVIDIA-related products, even more complex ones), a move up by one dollar in the underlying will cause (approximately) an increase of Delta = 54’589 USD.

In the second part of this article, we will focus on structured products Risk Business Intelligence (RBI), highlighting the power of aggregation (with a large set of Structured Products for a series of underlyings) to enrich the data and provide a deeper understanding of market exposure across its various dimensions.

_{Image: Adobe Stock}

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 Disclaimer

• This content is not intended as a solicitation or an offer; it is provided solely for informational purposes to professional investors
• The information presented herein has been prepared with great care; however, errors may still occur