Derivative Notional, Market Value, and Fair Value

# Derivatives: Value vs Notional/Principal amount


# Derivatives: Value vs Notional/Principal amount












I am reading "Options, Futures and other Derivatives" by John Hull. In chapter 1, a section on OTC market size has the following lines.

> Figure 1.1 compares (a) the estimated total principal amounts underlying transactions that were outstanding in the over-the-counter markets between June 1998 and December 2019 and (b) the estimated total value of the assets underlying exchange-traded contracts during the same period. Using these measures, the size of the over-the-counter market in December 2019 was \$558.5 trillion and the size of the exchange-traded market was \$96.5 trillion.

> In interpreting Figure 1.1, we should bear in mind that the principal underlying an over-the-counter transaction is not the same as its value. An example of an over-the-counter transaction is an agreement to buy 100 million U.S. dollars with British pounds at a predetermined exchange rate in 1 year. The total principal amount underlying this transaction is \$100 million. However, the value of the transaction might be only \$1 million. The Bank for International Settlements estimates the gross market value of all over-the-counter transactions outstanding in December 2019 to be about $11.6 trillion.

I did not understand how "value" is calculated. In case of options, there is a premium involved that could be the value, but here the example appears to be of FX futures. Its not profit since the transactions are still outstanding. Please help me differentiate "Value" from "Notional/principal amount".

More importantly, why not use "Notional Amount" to compare ETD and OTC markets? The numbers are sourced from Bank for International Settlements. Other free data sources on derivative markets also show data that is difficult to compare. See this question. It is usually mentioned that OTC markets are several orders of magnitudes larger than Exchange Traded markets. However, it "seems" that the sizes of ETD and OTC markets are not very different now.

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/79660

Hull's is not a good book to learn "the product". I'm not sure which one is, but not his for for sure. Maybe The Divine Proportions of Luca Pacioli by W.A.W. Parker is a good start? :)

An option is an instance of a financial contract, whose present value is what you'd need to pay/receive to enter into/terminate a similar contract now. Contracts, in turn, are an instance of assets.

Quants are sometimes tasked with building pricing models that value assets, typically more unusual ones. Quants have many other kinds of models besides pricing. Quants don't run Black-Scholes option pricing models all day, as some journalists write :)

I will adduce a simile that I heard many years ago from Emanuel Derman, which helped me understand what pricing models do.

Suppose that you own a house (the American dream:). Even if you're not looking to sell it right now, there are many reasons why an estimate of how much you might get for it might be useful.

Example 1. In much of the US, some local government official will sometimes very approximately estimate the market value of some property, and then the property owner will be forced to pay some property tax set as a fraction of its value. Note how the property's square footage can be accurately measured, and behaves a little like the notional here, in that if two properties are identical in most material respects, except for their sizes, then the ratio of their assessed values will be close to the ratio of their sizes. (In some jurisdictions, they don't use projected estimates, but only the last price for which the house was actually bought.)

Example 2. You want a home equity line of credit, in other words, you want to borrow some money, pledging the house as collateral. Or, you're divorcing your spouse, and need to divvy up the house. As part of the process, some independent real estate person will also estimate the value of your house using a more complicated model, taking into consideration the prices paid recently for nearby houses, and adjusting these prices for the differences between other houses and yours. Many, but not all, pricing models use similar principles. "A house down the block was recently sold for $\\\$n$, but they have granite counter tops in the kitchen, and you don't, so yours is $\\\$m$ cheaper."

Accountants talk about two kinds of values for an asset. A "fair value" is what you'd get if you try to unwind the asset under normal market conditions, and a "prudent value" is what what you might get under "fire sale" conditions. If you're "motivated" to sell your house quickly, you might agree to "prudent" lowball offer, rather than wait and hold out for a "fair" one.