Financial fiction: Pack's option

Finance fiction

After numerous conferences on the impact of regulation and the new market structure on quantitative finance, it’s time to start thinking about the impact the quants can have on regulation and the market structure.

The book not only covers theoretical considerations about the foundations of a multi-curve framework, and practical considerations about liquid instruments, it also contains directly or indirectly some "finance fiction" episodes where non-existent instruments or practices are described.

The reason to introduce such fictions in a non-fiction book is that the market is changing and is largely incomplete. Instruments that were completely redundant in the past are now becoming nice-to-haves or even must-haves. Changes in regulatory treatment, movement to futurization, generalisation of collateral and margining practices have created a moving ground. The financial landscape is moving; I try to guess some of the potential new characters.

After speaking at numerous conferences where the topic was something like "impact of the crisis/regulation on quantitative finance", I would like to start a new trend on "impact of quants on regulation/market structure". The indirect goal of those episodes is to influence changes in the direction of a more complete offering or simpler rules.

My first episode in that trend is:

Episode 1: Pack's options

Packs and bundles

A futures pack is a block of four consecutive STIR futures (1st to 4th, 5th to 8th, etc.). The packs are colour-coded, from the first to the tenth pack: white, red, green, blue, gold, purple, orange, pink, silver, and copper. The packs are traded as such on different exchanges; one trade creates positions in the four underlying futures. A futures bundle is a block of the first packs. A n-year bundle is a block of the first n packs, i.e. the block of the 4*n first futures.

Packs and bundles are traded on CME in USD and on LIFFE (and planned at NLX) in EUR and GBP.

A single futures contract is the exchange-traded equivalent of the OTC FRA; a pack is the equivalent (in terms of Ibor fixing involved) of a one year forward starting swap; and a bundle is the equivalent of a n-year spot starting swap.

Ceci n'est pas une option

New options on STIR futures have been added recently to the offering with mid-curve options now offered up to five years. Nevertheless the offering is still in some way incomplete. A single futures contract is equivalent to a FRA, a pack/bundle is equivalent to a swap. On the option side, an option on a future is the exchange-traded equivalent of the OTC caplet or floorlet. But where are the equivalents of swaptions and forward starting swaptions? This is certainly a missing instrument in the exchange-traded offering(1). It is not an option for traders to trade the equivalent of swaptions in the futures world.

Ceci n'est pas une pipe.

La trahison des images, René Magritte, 1928.

New option

Completing the missing offering could be achieved in different ways. Our suggestion for this episode is to create options on packs and options on bundles. To our knowledge none of these products are currently offered at any exchange. Given the push for more standardisation and exchange-traded products, the question is which exchange will be the first to offer such a product?

Messieurs les Anglais, tirez les premiers !

Attributed by Voltaire to the (French) Comte d'Auteroche at the battle of Fontenoy, 1745

The XXI century corporate warfare is probably not as courteous as the XVIII century real warfare, and there will probably be no similar offer, but the question remains open: who will shoot first?

What are the details of those options?

The options are characterized by an expiry date and a strike (denoted K below). The option is on a given pack or bundle (with n futures in the block) and can be of the call or put type. The option could be traded on a premium or continuous margin basis. As I personally prefer the margined options for futures, I describe here only the margined version. The options are traded in price⁽²⁾. A settlement/closing price is computed every day by the exchange; usually it represents the price at the end of the trading period. The profit (today's price minus yesterday's price) is paid immediately by the short party to the long party (obviously if the numbers computed are negative, in practice the positive flow takes place in the opposite direction). This is a usual futures-style margin process.

On the expiry date, the call (resp. put) long party has the right (but not the obligation) to enter into a long (resp. short) position in the n futures underlying the pack/bundle. This is an all-or-nothing option; the exercise is for all the futures in the block; the exercising party cannot select which futures in the block are exercised and which are not. The futures exercised are obviously fungible with standard STIR futures. The price at which the futures are entered into is the same for all of them in the block and is K.

If we denote by Fⁱ the price of the i-th future in the block, the pay-off can be written as

Sum_i=1ⁿ (Fⁱ- K)

Why a new product?

Given the inertia around any new product, especially in very standardised settings, we need a compelling reason for a new product.

Let me start with the non-compelling reasons. Those reasons are technical. The existence of a larger class of options, i.e. adding a pack's options to the futures, vanilla options and mid-curve options will enrich the calibrating instruments of models. This is important to price exotic options that depend on the correlation structure between LIBORs at different dates. Currently those options are not represented in the exchange-traded world.

But who needs exotics today?, I hear you ask. My answer is that new regulations are imposing exotic structures to standard products, like some path dependent caps and floors on mortgages, or timing adjustment on rolled deposits (LTRO), etc. One has to define "exotic": in the sense used here, it is not related to liquidity but a technical term meaning we need a dynamic model and a non-trivial numerical procedure to solve it. Enter into this category a lot of liquid products: bond futures (delivery option), FRA (FRA discounting), and change of collateral/margin. A lot of liquid products are, in the sense used here, exotic products.

The main reason for creating the new product is to fill a gap. The interest rate option market is important as very popular types of mortgages are fixed rate prepayable (the borrower has the option to repay his mortgage) or floating rate with some kind of cap/floor (potentially path dependent). A liquid exchange-traded market for options is useful. Currently that market exists only partially. Options on STIR futures are very short-term options of the cap/floor type, mid-curve options extend to underlying up to 5 years but are also very short-term expiry and on specific rates, not on a block of them. Offering options on packs and bundles would give more flexibility for hedging and expressing views. Options on bundles would be similar to swaptions and options on packs would be similar to options on forward starting swaps. The swaptions are the most liquid interest rate options in the OTC world. The reason of the liquid market on swaptions is also valid for a liquid market on the pack's options.

STIR futures are offered only to 10 years, with a lot less liquidity above 5 years. The interest on the pack's options would be mainly on the short to medium term sectors. For options on long-term rates (up to 30 years and maybe 50 years), another product would be required. But discussing that issue requires multiple new episodes, one for a "clean" swap future and one for the options on them.

And the pricing?

A technical discussion on how to price options on packs and bundles in a stochastic basis model is proposed in the book (Chapter 7, Section 8). In summary, in a Gaussian one-factor HJM with simple stochastic spread, the approaches used for swaptions and STIR futures with stochastic spread can be combined. If the products are becoming liquid, a model with smile dynamic would need to be developed, but that would be a non-fiction episode conditional to the realisation of the fiction.

(1) Some options on swap futures exist, but they are mostly illiquid. Some options on deliverable swap futures (DSF) may be added in the future, but for this the creation of a "clean DSF" is required. That in itself is another finance fiction episode.

(2) The term price for (options on) futures is a misnomer as the price is never paid; a term like "reference index" would be a better name. See also the introduction of Chapter 8 in the book for more on the subject.

Edit (13 August 2014): A slightly modified version of this blog appeared on OpenGamma's blog under the title: The Impact of Quants on Regulation and Market Structure.