## The London workshop August 20th-23rd 2015

I’ve been building right now and I don’t like to talk much when that happens, which is why no posts have been made recently. But SpecMat readers who are in London’s wheelhouse may be interested in RH’s London workshop. SpecMat will be there, especially since we’re now ‘doing’ financial engineering for the distributed capital services wing of RH. Here’s the program -should be cool.

## What is Additivism? (part I of II)

Just watch this video, like I have 4 or 5 times, and ask yourself the question “what is additivism?”

The student of nonlinear dynamics immediately thinks of additivism as a conservative concept.

In a linear system, the total effect of the combined action of two or more operations is merely the additive superposition of the effects of each operation individually. So where additivism prevails, the principle of superposition holds, and the system in turn is restricted to a graduated, quantitatively lower or higher behavior, but at any rate is always qualitatively the same, it remains unchanged, viz. a change by degrees that does not produce a new change in kind.  And as Ed Lorenz often liked to observe, linear systems have two choices: they either remain locally-bound or they fly off to infinity.

By contrast, in a nonlinear system, the combined effect of two or more elementary operations can induce dramatic effects, disposing the system of new solutions whose availability were previously latent or unactualized. Here one observes perhaps even an incremental change by degrees, but which suddenly produces a new change in kind. The divergent evolutionary process of difference by way of repetition, topological folding and twisting, nonorientability -these are all the kinds of system-behaviors cooked into nonlinearity.

My sense is, after watching the video, thinking (which I like to do sometimes), and reading up on their cookbook project, that Additivism self-understands itself to be wagering on nonlinearity -and yet there’s that term, “additivism”.

So my question is, what, prey-tell (that’s not a typo -come on people let’s distribute a new meme!), is additivism?

## What will financial derivatives markets look like on the Ethereum blockchain?

Nobody knows the answer to the question, ‘what will financial derivatives markets look like on the Ethereum blockchain?’, but Spritzle is a going be talking about this on Thursday, April 2nd, at Galvanize, in San Francisco. SpecMat will be there, and will or will not be reporting back on it, relative to its level of ‘compelling-ness’.

## Exotic Options as Smart Contracts

“Get out of the sun or you’ll die!”, cried the Lizard, “there are only two possible options, here!”

“Not for me”, replied the Mammal, “evolution has written me a new possibility –I can regulate my internal body temperature.”

“How is this possible?” asked the Lizard, marveling at the notion that what was once impossible for all animals was now possible for the Mammal.

“Well, I’m not exactly sure”, answered the Mammal, truthfully.

“I know how”, offered the biologist.

The two animals turned towards her…

There are persons, including us here at Specmat, who find themselves compelled to think-on and tinker-with second generation blockchain capacities. They share in common the ‘sense’ that combining the algorithmic art of cryptography with digitally-distributed public networks now enables us to write new protocols, which secure new kinds of relationships, whose endogenous capacities greatly exceed the limits of what was previously possible. It’s not so much that smart contracts written on a blockchain to create distributed applications (Dapps) now awaken us to new possibilities, as it is the case that these technologies have actualized a new set of possibilities which were previously nonexistent, and it is therefore up to us to awaken to, examine, and understand this fact, in order to think-on and tinker-with, and deploy their powers.

Nick Szabo, so far as I can tell, coined the term ‘smart contracts’. In his classic essay on the topic, he defines them: ‘Smart contracts utilize protocols and user interfaces to facilitate all steps of the contracting process…The basic idea behind smart contracts is [thus] that many kinds of contractual clauses (such as collateral, bonding, delineation of property rights, etc.) can be embedded in hardware and software we deal with…’[1] This seductively simple notion has profound capacities when deployed on a digitally-distributed public ledger, called a blockchain. In fact, whether Nick Szabo is or is not Satoshi Nakamoto is probably beside the point at this time. We’re currently witnessing the progressive differentiation of an era of second generation blockchain technology, wherein Ethereum and Eris Industries, among others, are developing and enjoining us to develop with them the unbounded number of new protocols which smart contract-enabled Dapps on a blockchain make possible. And here at SpecMat, as we’ve said before, we believe nothing is more suitably commensurate with the wagers of second generation blockchain technology than the second generation options technology called exotic options.

Let us evaluate this claim.

Channing starts a goodserv

Channing believes she has a good idea for a start-up goodserv.

The first thing Channing must do is publicize her goodserv’s existence. She does this by registering her goodserv’s name and product with some Dapp, whose protocol is a distributed name registration database (a kind of Namecoin-equivalent), to which any first-to-file registrant who wishes to start-up a goodserv can go to register her goodserv’s name and product.

Channing registers her goodserv on this Dapp. Now Channing’s goodserv has been made public on blockchain.

The next thing Channing wants to do is fund her start-up. She needs to raise some funds to get things going. The most common method of raising funds is to take out a loan, or some other form of debt (e.g. a bond, a note, some commercial paper). But she’s reluctant to ‘go into’ debt to do so, since she knows this indefinitely indebts her goodserv’s unknown future market value to its present notional value, which is currently at zero. The other common method of getting seed money is to issue equity, so this is what she wants to do; but given the fact that Channing can’t issue ‘stock’ in a goodserv that doesn’t yet exist, and even if she could, she doesn’t want a set of sedentary ‘shareholders’ extracting the future surplus from her goodserv’s net profits, but rather would prefer to enfranchise ‘stakeholders’ working with her towards the mutual, shared success of their common venture –which is, namely, Channing’s goodserv. This means that Channing, in other words, is both aesthetically- and philosophically-disinclined to issue stock, so she will not be selling stock in her goodserv at this time.

What else can she do? How can she fund her start-up costs?

The answer is, Channing will write and sell exotic options. And she will use the cash from their sale to fund the start-up of her goodserv.

Writing Optionality

Exotic options are a second generation class of options. Options comprise a class of financial derivatives. Financial derivatives comprise a class of financial assets. Financial assets are commodities that can be bought and sold like anything else. The difference, however, is that anyone can write an option ex nihilo into existence, without having to first own anything whatsoever. To write and sell an option is simply to create and sell for a fee optionality to someone else; and to buy and hold an option gives its holder optionality.

There are two kinds of options. There are ‘call options’, the holding of which gives one the right to acquire something for a certain pre-agreed to price (called the ‘strike price’ K), on or by a future date (called ‘maturity’ or ‘expiration’). And there are ‘put options’, the holding of which gives one the right to part with something for a strike price K on or by expiration. Common financial markets practice is such that this ‘something’ which the call/put holder has bought the right to acquire/part-with is a stock, or some other standardized financial asset. Let us include this notion, but also broaden its scope of possible objects so as to include anything produced by a goodserv.

We have said Channing is going to fund her start-up by writing and selling exotic options. She is therefore someone who ‘operators’ optionality. She is writing optionality. She is creating optionality ex nihilo, and potentially ad infinitum (though this latter phrase, of course, is just a manner of speaking).

Operators are persons who write and sell, and buy and read options. Operators trade optionality. An operator will therefore need to keep a ‘book’, which houses her total portfolio of assets and liabilities: it will contain options which are written and sold (liabilities) and options which are held and may be read (assets), as well as any synthetic assets, cash-currencies, and any referent assets. These contents of an operator’s book are stored at a digital address, which is secured and managed by a smart contract on blockchain.

In life, everyone wants options. The state of having options is called optionality. Options are a financial technology for creating and selling optionality. And operators on a blockchain can now write and read options, and will be constantly reading and writing optionality anew.

What we have just said equally applies to exotic options or vanilla options; these are the two classes of options. Vanillas are standardized, and conventionally-structured, and it is true that today ‘anyone’ can trade them, even without a blockchain, smart contracts, or Dapps. For example, today if you were to register (for a fee) in order to apply (for a fee) for an options account (on which you pay a fee) to begin trading options (for a fee) on one the many options brokerage houses, you will most likely only be buying and selling vanilla options (for a fee), and will not have the opportunity to write or read exotics (or if you are able to, there’s a big fee you’re charged). Exotics are bespoke, customizable, and have unconventional structures. And if managed by a Dapp as a series of smart contracts on a blockchain, there would be little-to-no cost for anyone to begin writing and reading options. You’d also immediately have a distributed space, with a self-authenticating, secure public ledger, which would be nothing less than (but also more than!) an autonomous space for transactions that is presently known and defined as a ‘market’.

Exotics as Smart Contracts on Blockchain

So let us first understand these two terms, ‘smart contracts’ and ‘blockchain’, and then we’ll consider their use-value for Channing’s attempt to fund her start-up with without indebting herself, but rather by writing and selling for a fee some optionality on her start-up’s future value.

The most general acceptable definition of a smart contract is a user-agreed-to customizable rule or set of rules which governs case-specific interactions of the users of a blockchain. These interactions, like all interactions in life, produce and are comprised of arbitrary data.

The most general acceptable definition of a blockchain is a digitally-distributed space for the time-stamped storage of arbitrary data.

Like many profound technologies, both of these things sound remarkably simple, and in truth they are: the ‘arbitrary data’ stored on a blockchain could be the content and terms of an economic transaction between two or more parties, the amount of money in an account, the results of casting and tallying votes, or any other arbitrary data that one can imagine, or that two or more people might produce, or require to govern their interactions.

However, when the distributed technology of a blockchain is combined with the hyperflexible, fully-customizable technology of smart contracts, all of the blockchain’s opt-in users are immediately equipped with an interminable, modifiable, secure mechanism to convene, deliberate, vote, and implement agreed-to rules and permissions to create and modify data, through a set of self-administering and self-executing scripts. And these scripts can literally be anything, their potential is unbounded: any user-agreed-to consensus or security rules can be used to manage the blockchain. Once they’re written and agreed to, the scripts are then time-stamped, executed, and publicly registered on the blockchain. They are smart contracts.

Ok, fine. So let’s consider how Channing and her prospective equity partners could use a smart contract on a blockchain. There are a few exotic options that immediately come to mind (though by no means exhaustive), which Channing wants to write and sell. The first exotic she notifies prospective investors she’s willing to write is the following:

Example 1. Compound Options

Compound options are options on options. They are ‘compoundings’ of risky and therefore relatively inexpensive options within which are embedded one or more comparatively more expensive and ideally less risky options.

For instance, if investor R buys a call option on a call option on Channing’s goodserv, R has bought for the premium price of C1 the right to pay the first strike price K1 by the first exercise date T1, in order to receive a second call option C2, which then gives R the right to buy some referent asset A which Channing and R have agreed to ahead of time (and which is written into the terms of the contract) for the second strike price K2, by the exercise date T2. What is this reference asset? Maybe it’s the product or service Channing generates with R’s start-up funding. Maybe it’s a share of her goodserv’s value. Maybe it’s another call option. Maybe it’s a put option. Maybe its cash, which Channing’s goodserv will eventually generate. –But that’s the point: it can be literally whatever Channing and R agree to as the referent.

Why would Channing want to write and sell a compound option?

First off, Channing just needs some fast seed money to give her a chance to pay for her initial start-up costs. By writing and selling a call on a call to R (and other R’s), Channing acquires some immediate start-up funding, earned from the premium price of the option C1. If, after T0, Channing changes her business model, can’t get her act together, or suffers some set-back between T0 and T1, it’s likely R will not exercise the option for the premium price K1. On the one hand, Channing might be sorry to see R not exercise the C1 option by its expiration at T1, since this means she’ll now be lacking the subsequent second-stage funding she would have otherwise acquired, had R been willing to exercise this call option at the price of K1. But on the other hand, Channing owes nothing to R in return. She can walk away debt-free. She owes nothing to no one. She can try something else sometime in the future. However, if Channing makes good use of the funding she acquires by selling C1 to R; and if R sees this; it’s likely that R will either exercise C1 for the additional price of K1, which now gives R the C2 right to buy some reference asset A for some additional price they agreed to ahead; or R could also sell C1 before T1 to some other R, who will exercise C1 for the price of K1. Channing is probably ambivalent as to which of these occurs, since either way Channing is provided with additional start-up funding.

Why would R want to buy a compound option from Channing?

R has familiarized herself with Channing’s goodserv proof of concept, and either really likes its proposal, or at least believes it deserves a chance to succeed or fail on its own merits. But R doesn’t know what the future holds for Channing’s gooderv: it could be the next ‘big thing’, or it could prove unviable and fail. R does not want to lose too much money when taking a risk on Channing’s start-up, but R does want the option to invest in Channing’s start-up now, and possibly even invest more in the future. And after all, if Channing’s goodserv turns out to be successful, shouldn’t R be reasonably remunerated for believing-in and investing-in Channing’s start-up, when no one else would? By buying from Channing a relatively inexpensive call on a call for the premium price of C1 on her goodserv, on the one hand, R will not lose more than the initial premium price of C1, since if by T1 R is dissatisfied with the progress of Channing’s start-up, R simply lets the option expire unexercised, or possibly even tries to sell the option to someone else before T1 to try to recover as much of the C­1 money has possible. But on the other hand, when at T0, R pays the initial premium price C1, R is also acquiring the option to either exercise the option by T1 for K1, in order to now pay a new (and inevitably more expensive) premium price C2 to acquire the new (and more valuable) right to exercise the new call option C2 at T2 for K2; or once again, R could also sell her C1 option to someone else now for a profit, and simply walk away. If Channing’s goodserv begins to experience some success, or if R is otherwise satisfied with its progress, R is financially and/or psychologically remunerated for the early risk she’s taken. But if Channing’s start-up does not succeed, R has not lost very much money. R is not broke. R is not disillusioned. R can invest in something else sometime in the future.

In essence, then, a compound option allows both Channing and R to tailor their contract so as to mutually and equitably benefit from the success of this venture. It gives both of them some optionality. R is invested in Channing’s success. But R need not go broke wagering on Channing’s goodserv. Likewise, Channing is grateful for R’s early support, and is happy to try to reasonably remunerate R for wagering on the future success of her goodserv, when no one else would; but in no way is Channing’s prospective future interminably indebted to R.

However, compound options are only one method by which Channing writes and sells optionality to fund her start-up. She could also write forward start options, chooser options, or barrier options, and there are so many other exotic options as well. Let us briefly consider a few in closing.

Example 2. Forward Start Options

Forward start options are options that will start at some time in the future. The nature of Channing’s goodserv may be such that it will take some time to begin monetarily demonstrating its progress. By writing a forward start option, Channing can write and issue an option to fund the initial stages of her venture, without being compelled to immediately produce any nominal value. And R can hold this option without its value experiencing ‘time-decay’ (theta) as the date of its expiration nears.

Example 3. Chooser Options

Channing could also write a chooser options. After a specific period of time, the holder of a chooser option can ‘choose’ whether their option is a put or a call.

Example 4. Barrier Options

Channing may need to hire employees, in order for her goodserv to succeed. Channing could pay her prospective employees with barrier options. The payoff on barrier options depends on whether the referent reaches some pre-defined price point during a set period of time. This is a method of equitably-enfranchising those who may want to work with Channing towards the common success of her goodserv startup: if they do good work, they will be remunerated by the rise in value of their option; if they do not do good work, the value of their option will decline.

Channing can do all of this by easily downloading an application on her smartphone or computer, which allows her to advertise and customize the writing and selling of any of these four types of exotic options. A liquid market in exotics options will ultimately reduce transaction costs for both parties, and improve its market stability. But already from the beginning, if these exotics are executed by Dapps, written as smart contracts, and transacted on a blockchain, there is no reason for there to be anything but the most marginal of costs even from the outset.

But this is only one possibility. In a future post, SpecMat will examine how to englobe these Dapps within a DAO, by constructing a universal synthetic CDO.

For the Mammals we are….

[1]“Formalizing and Securing Relationships on Public Networks”, Nick Szabo, First Monday, No. 9 Sept. 1997

## Hey kids, do you like rhizomes?

Recent years have introduced profound evolutions in web technologies. Most significantly are new differentiations in blockchain technologies –namely, smart contracts, decentralized applications, and decentralized autonomous organizations.

Smart Contracts. Already in the early 1990s cryptographer and legal scholar Nick Szabo observed that combining digital protocols with user interfaces facilitated the creation of decentralized systems of contracts to hold, move, or divide-up any number of different classes of assets according to any rules pre-agreed to by its participants.[1] The problem, of course, was that no web technology actually then yet existed which were capable of addressing the complex of issues (e.g. the infamous “double-spending problem“, etc.) any attempts to implement an absolutely rhizomatic economy would convoke.

Enter the Blockchain. Then in 2009 Satoshi Nakamoto introduced the first fully-decentralized digital currency, known as the bitcoin, which enables peer-to-peer transactions wherever there’s internet access. Until recently, media attention has focused on issues such as its absence of a central issuer or backing by a national bank, its price volatility, and possible uses in criminal activities. In truth its radical innovation lies less with these issues, and even less with the bitcoin itself, than with the concept of the blockchain. Economic transactions in a blockchain consist of the digital transfer of money or some other unit of value for goodserv: these transactions are collected in ‘blocks’, and then ‘chained’ together, comprising a visible, verifiable, digital, decentralized public ledger. For this reason, any coupling of operators, however diffuse and heterogeneous, using a blockchain to organize themselves are immediately an autonomous, digitally-distributed, fully-decentralized consensus system, equipped with mechanisms for public memory, voting, and agreement on the order and character of all transactions –and importantly, therefore now with neither any need nor place for a centralizing authority. This, dear denizens of dromocracy, is a rhizome.

Bitcoin inaugurated the first wave of blockchain ledgers. What is now being called ‘the second-wave’ in blockchain technology underscores the realization that a blockchain can do much more than simply process coin-based transactions. In fact presently, what’s less clear are its limits. Even before the second wave, already in 2010, for example, Namecoin was applying Bitcoin’s consensus protocol to develop a decentralized name registration database, in which a first-to-file registrant wishing to start a goodserv (goods and services), e.g. “Channing’s Organic Greens”, or “Serra’s Eco-Architecture”, simply creates an account, which is timestamped on the blockchain ledger, and their start-up has now been publicly ‘named’ into existence.

Of course, this still begs the question of how Channing and Serra will fund their startup, without either already holding the necessary amount of cash, or else securing outside credit, which is to say going into debt, i.e. becoming a debtor, indebting themselves, their future work, and its future value in advance to some creditor? Can an independent goodserv startup be born without debt?

It can. Channing and Serra can do this. How? In short, through OTC writing and sale of exotic options (this is the topic of soon-to-come future post). Presently, of course, there is no venue for anyone -let alone Channing and Serra- to deploy this technology for purposes of starting a non-indebtified goodserv.

This is why I like Ethereum (Vitalik’s white paper is here) and their offshoots, e.g. Eris, etc.. Ethereum is currently the apex of second wave blockchain. It has developed a built-in Turing-complete programming language, equipping its users with a ready ability to create any variety of smart contracts. This means any two local operators can deliberate, agree-to, and create a short term contract to exchange goodserv or some financial asset for coin. And any larger set of operators can deliberate, agree-to, and create a long-term contract englobing the local operations. This amounts to now a fully-equipped operational capacity for a series of decentralized applications (Dapps) englobed within a DAO –a series of local and terminable smart contracts within a universalized and interminable, but always modifiable, decentralized autonomous organization. This means we now have the ability to actualize an absolutely rhizomatic economy, comprised of clusters of operators of exotic options, englobed within a universal synthetic CDO: in a word, dromocracy.

For this reason, over the course of the next several months, SpecMat will be examining blockchain and affiliated technological concepts, and ultimately collapsing them into our ongoing Dromocracy project.

[1] Nick Szabo, “Formalizing and Securing Relationships on Public Networks”, First Monday, Volume 2, No.9, September 1997, http://firstmonday.org/ojs/index.php/fm/article/view/548/469#introduction

## The Greek Election by the Numbers

Here at SpecMat we’ve been meaning to evaluate the financial implications of Syriza’s victory in this weekend’s Greek elections. However, we’ve elected to not do this, but in lieu have provided some “numbers” to lend one’s attempt to nonnumerically do this for oneself. Briefly:

265. At \$265bn, Greece’s economy is slightly smaller than that of the city of Philadelphia.

162. The leftist Syriza party resoundingly won this Sunday’s Greek election. They formed a governing coalition with the the right wing Independent Greeks. Together they control 162 seats of the 300 seat Greek legislature.

49. Panos Kammenos is the party leader of the Independent Greeks. He is opposed to gay marriage and civil unions, does not recognize the separation of church and state, wants to lower taxes on the rich (naturally, to stimulate economic growth), and is virulently anti-immigration/antiimmigrant (e.g. believes children of immigrants residing in Greece at birth should be denied citizenship). He’s 49 years old.

4. Kammenos often refers to Germany as the “Fourth Reich”.

5 and 2. Over the past 5 years, the government of Greece has agreed to endure “austerity” (a code word for gutting the public sector, e.g. slashing public programs, laying off public employees, etc.) in exchange for 2 international bailouts.

269, or 240 (and rising) . Alxis Tsipras is Syriza’s party leader (and likely new prime minister of Greece). His party’s campaign was staked on rolling back fiscal austerity demanded by Germany (and the troika) in return for \$269 bn in bailout funds received by Greece.

2 3 15. Europe’s bailout plan for Greece expires on February 3rd of this year.

2, not 4.5. Syriza wants to run a budget surplus of 2% rather than the agreed to 4.5%.

90 days and 20. Greece’s stock market has lost 1/5 of its value in the past three months (not to mention the several billion euros withdrawn from Greece’s banking sector in anticipation of Syriza’s increasingly certain victory).

7.9. Greece owe’s \$7.9 bn in bonds to the ECB in July and August of this year.

0. There is currently no money in the Greek treasury to pay back the ECB. Without a renewed aid package in return for more or at least continuing austerity, Greece will default (-or print drachmas?)

19 or TBA. There are currently 19 Eurozone member countries.

## What Black-Scholes-Merton means to a speculative materialist

### Lesson Two

Even those persons paralyzed by anxiety over their lack of knowledge of financial economics will intuitively grasp that uncertainty pervades an attempt to ascertain what will have been the value of an asset in the future, relative to its subsequent past value now in the present. Can this even be done? BSM says it can.

Initially BSM announced itself as a risk-neutral, nonarbitrage model for pricing options. We will later expand on the importance that BSM isn’t quite used like this today. But let us presently observe that BSM is indeed a nonarbitrage model, albeit one whose condition of possibility and goal is arbitrage. However, BSM asserts that when deploying its partial differential equation to determine the value of an option, i.e. in order to know in the future what will have been the value of an option today, an operator must know four things:

(i) the option’s time to maturity (T)

(ii) the riskless interest rate (r)

(iii) the referent price (S0)

(iv) the volatility of referent price (σ)

The first three parameters are easily found. They’re either quoted in the market, or in the case of the first parameter, (T) time to maturity, i.e. the option’s expiration date, is written into the terms of the contract itself. However, the fourth parameter, volatility, is a bit trickier. BSM presumes a normal distribution, or ‘constant’ volatility –which amounts to erecting a thin epistemological wall to artificially insulate its model from jumps, irregularities, or volatile volatility, hoping those hideous animals on the other side won’t breach its perimeter, and stroll right in. Is to know volatility ontologically impossible? What even is volatility?

These queries have no quick redress, but are crucial for grasping the model of economy of deterministic chaos that is dromocracy proposed by D&G, and which in 2014 we have been and will be continuing to elaborate. Let us then move through its logic, or at least of it what we presently know.

If markets make a random walk, so too are plots of trajectories of the price movements of its assets, whose economic properties orbit along their markets’ surfaces. This means volatility is stochastic, unsteady, intractably irregular, a dark beast –and therefore this fourth parameter that an operator ‘must’ know to use BSM exhibits some determinism, yes, but a determinism wholly infused with chaos, or even is chaos.[1] Time spent studying the behavior of any class of financial asset causes quick realization that data on ‘past’ or ‘historical volatility’ (also called ‘actual volatility’)[2] is available but not dispositive for knowing future price movements. So any attempts by a BSM operator to divine ‘future volatility’ amounts to an attempt to solve a differential equation by way of a nondifferentiable function (*it can’t be done). Operators know this, and for this reason elect to retain BSM, but invert its equation to iterate ‘implied volatility’. Doing so, an operator must still know four things:

(i) the option’s time to maturity (T)

(ii) the riskless interest rate (r)

(iii) the referent price (S0)

(iv) the volatility of referent price (σ) (iv) the market price of the option

…but all four of which are now dictated or conveyed by the market, are messages transmitted in and by the market: the new fourth parameter is combined with the previous three parameters, and now used to derive the as-yet-unactualized volatility implied by the current market price of the option. The BSM operator, then, no longer plugs in the parameter of a normally-distributed volatility, which is to say a ‘constant’ volatility presumed to be actual, actualized, or ever actualizable, in order to derive the theoretical value of an option, but now plugs in the market price of the option to derive the theoretical value of volatility –i.e. the virtual value of volatility that an actual option price implies. Does this not render implied volatility a partial relic of the virtual that’s yet now paradoxically actual as well? In a future post we will take up this technological issue by opening up, to briefly peer inside, the peculiar material profundities interpellating implied volatility, which we believe is an intensive economic property: an odd, rare empirical instance of a differentiated aspect of the virtual that’s been refracted through itself and now dumped out into actuality; giving rise to ‘actual volatility’ at the same time such actualization of the latter covers or cancels it out.[3] Moreover, some attention directed to the robust Deleuzian-dynamical systems theoretic sense of the concept ‘intensive’ organically breeds our conviction that implied volatility is readily deployable as a fungible pricing mechanism, far more commensurate with the economic institutions and endemic behaviors of the denizens of a dromocracy, than that base and placid, one-dimensional, extensive medium of exchange we call ‘money’.

Presently, our brief tutorial on options will presume little background on our reader’s part.[4]

Financial derivatives comprise a class of financial assets. Options comprise a class of financial derivatives. In dromocracy, the exchange of options, especially exotic options (or simply ‘exotics’) comprise its principal class of exchange. Contingent local communities of becoming are ‘clusters’, rendering ‘clusters of exotic options’ (CEOs) one of its two economic institutions (the second being a universal synthetic CDO, to be outlined a bit later). In dromocracy, exotics among clusters are traded en masse.

The standard, if only sometimes correct definition of a financial derivative is an asset whose value derives from some other asset, often called a referent or underlier.[5] We’re supposed to tell you this; but it need not overly concern us, and at any rate, like the principles of Euclidean geometry, is not so much always wrong as it is only sometimes true. Our real concern is that an option is a nonlinear financial derivative producing a contingent claim; and that holding an option gives one the right to do something by a certain date, it gives the option holder choice, or optionality. Taleb tells us that ‘optionality is a broad term used by traders to describe a nonlinearity in the payoff of an instrument’[6], which will be particularly compelling to a reader who is now beginning to cognitively synthesize that rhizomes-nonlinearity-chaos-financial derivatives are the constitutive components of dromocracy, and that such novel model of economy is available to us if we so choose.

There are two kinds of options. There are ‘call options’, the holding of which gives one the right to acquire something at a certain price (called the ‘strike price’), on or by a future date (called ‘maturity’ or ‘expiration’). And there are ‘put options’, the holding of which gives one the right to part with something at a strike price on or by a future date. The terms ‘European’ and ‘American’ have nothing to do with where the options are written, read, or otherwise exchanged. Rather, European options can only be exercised on the day of their expiration, while American options can be exercised any time between their inception and expiration.

‘Operators’ are those persons exchanging options. Operators trade optionality. There are two types of operators: ‘writers’ and ‘readers’. To write optionality is to compose and sell an option for a fee to a reader, who now holds the right to choose to acquire some pre-agreed-to asset, whether an object or service, at a predetermined price, if mutually-pre-agreed-to conditions are met either at maturity or during the life of the option. To read optionality is to buy an option for a fee from a writer, who now accepts liability to deliver some pre-agreed-to asset, whether an object or service, at a predetermined price to the reader, if mutually pre-agreed-to conditions are met either at maturity or during the life of the option. Writers, then, issue optionality for a price, and accept liability if conditions written into the option are met. Readers accept optionality with a price, and exercise their choice if conditions written into the option are met.

What we have just said equally applies to exotics or vanillas, which are the two classes of options. Vanillas are standardized, and conventionally-structured. Exotics are bespoke, and have non-conventional structures. However, we will principally concern ourselves with exotics. It worth noting here, to begin, that pricing exotics can quickly become quite complicated in ways not conquerable by however-sophisticated modeling techniques, therefore generating available arbitrage opportunities for its operators. Importantly, this is due to exotics’ high-degree of nonlinearity: vanillas, yes, are already nonlinear, since all options are nonlinear assets; albeit exotics exhibit a higher degree of nonlinearity, as we will show. Exotics are to be the principal class of options exchanged in a dromocracy.[7]

BSM’s original assertion is that in theory it’s possible to construct a riskless portfolio, comprised of a position in options and some referent, such as stocks (though it could be any generic asset). We henceforth call this portfolio a ‘package’.[8]

Scholes says, ‘Black’s and my discovery was how to price options and to provide a way to manage risk.’[9] Derman and Taleb remind us this doesn’t mean that options are rendered riskless assets, or that an option’s actual price movements are in any way predictable, periodic, or nonstochastic.[10] Rather, the success of BSM’s pricing model pivots on hedging. And not just any hedging, but delta hedging –whose wager is that if an operator can get the delta of their package ‘right’, and then hedge accordingly and continuously, any price movements in an option position will always be offset by price movements in the referent position, and vice versa: and that these price movements offset one another means that the delta of the package at any given point in time, while not strictly zero, is nonetheless always striving towards it, tending towards it, asymptotically ever attempting to move yet closer to zero. The delta of the package is perpetually a becoming-zero.

[1] We’ll see that the issue is more involved than this. The initial model of price behavior used by BSM assumed that price changes are stochastic and normally distributed. To simply assert that a process is ‘stochastic’, or random, only further begs the question of the order and degree of its randomness –there are, after all qualitatively different classes of stochastization, so that any identification of a process as random must clarify to what class of randomness the process belongs (e.g. a Markov, Wiener, Itô, or Deleuzian process)? The answer given by BSM is that volatility exhibits a randomness that is normally-distributed, which makes it a Weiner process, but which turns out to be problematic. Today the standard financial economic definition of its class of stochastization is an Itô process, which we will show is also problematic.

[2] Our reader will be reminded that the three registers of reality in Deleuze’s ontology are actual-potential-virtual. ‘The actual’ is simply that which ‘is’ differentiated (what is sometimes mistakenly labeled ‘reality’). ‘The potential’ also is that which ‘is’, albeit only ‘is’ as a possibility (Deleuze identifies the potential as that which is subject to a probability distribution, but whose possible outcomes are therefore predetermined by the interlocutions of the actual and virtual). ‘The virtual’ is neither actual nor potential, and yet it exists ‘in reality’ nonetheless. A good deal of Deleuze’s project is to make technical recourse to mathematics and sciences to illustrate that while neither actual nor potential, the virtual comprises another register of reality altogether –a register structuring the space of what is possible to become actual.

[3] It is far from evident this notion is wholly comprehensible in Deleuze’s ontology. Its presentation, however, is far from a foreign element in his house. On the one hand, Deleuze toes the standard dynamical systems theoretic line that intensive properties often or always are canceled in those systems in which their spatiotemporal dynamisms generate the actualization of the extensive properties, whose very generation cancels them out. For example (‘There is an illusion tied to intensive quantities. This illusion, however, is not intensity itself, but rather the movement by which difference in intensity is cancelled. Nor is it apparently canceled. It is really canceled, but outside itself, in extensity and underneath quality.’) Difference & Repetition pg. 240; and (‘Intensity creates the extensities and qualities in which it is explicated….It is nevertheless true that intensity is explicated only in being cancelled in this differentiated system.’) Ibid pg. 255 Also see Ibid pg. 228. However, on the other hand, Deleuze’s (and D&G’s) special interest in complex, high-order, nonlinear chaotic systems (i.e. ‘systems of difference’) is their explication of relics of the virtual, e.g. intensive properties, whose logic can then be traced back up through the actual, and tinkered with. After all, why map, e.g. in phase space –if not to then tinker with matter’s evolutionary capacities? For example (‘it is in [systems of] difference that…phenomena flash their meaning like signs. The intense world of differences…is precisely the object of a superior empiricism. This empiricism teaches us strange “reason” [read: strange attractors], that of the multiple, chaos, and difference.’)

[4]The best book on options for the nonspecialist is John C. Hull Options, Futures, and Other Derivatives, Prentice-Hall 2009. For this reason, on our reader’s behalf we draw on Hull throughout Part IV.

[5] For example (‘A derivative can be defined as a financial instrument whose value depends on (or derives from) the values of other, more basic, underlying variables. Very often the variables underlying derivatives are the prices of traded assets. A stock option, for example, is a derivative whose value is dependent on the price of a stock. However, derivatives can be dependent on almost any variable, form the price of hogs to the amount of snow falling as a certain ski resort.’) Hull pg. 1; and (‘A derivative is a security whose price ultimately depends on that of another asset (called underlying). There are different categories of derivatives, ranging from something as simple as a future to something as complex as an exotic option, with all shades in between.’)Taleb pg. 9

[6] Ibid pg. 20

[7] In dromocracy there are two types of markets, ontologically-speaking, whose materiality is bound as one: there are commoditized products, which have standardized agreements in place to eliminate non-template inconveniences, and range from simple ‘spot-priced’ classic objects (e.g. things to eat and wear), to low-order forms of exotics (e.g. single barrier knock-outs); there are also nonstandard products, which are wholly exotic, and whose payoffs are specific to the instrument –these comprise the majority of contracts for work relations for the denizens of dromocracy. With such exotics, everyone is constantly tracking their Greeks. We thus agree with Taleb’s itemization of the basic difference between commoditized and nonstandard products, when he observes that ‘the real difference between [the two] is that one type is tailor made, with [higher risk and volatility, and] smaller traffic, while the other has features of a discount store with standard sizes and prices, but a higher volume.’ Taleb pg. 51

[8] Hull (2009) defines a conventional package (‘A package is a portfolio consisting of standard European calls, standard European puts, forward contracts, cash, and the underlying asset itself.’) pg. 555. We will ultimately wish to tailor this general concept to include an individual’s total portfolio of assets –generic and synthetic, comprised of exotic options and CLNs, as well as the synthetic assets whose total notional value comprises an individual’s universal synthetic portfolio, which is why we have neologized the term herein.

[9] Myron Scholes, “Derivatives in a Dynamic Environment”, The American Economic Review, Vol. 88, No.3, June 1988 pg. 351

[10] Emanuel Derman and Nassim Nicholas Taleb, “The Illusions of Dynamic Replication”, first draft Apr. 1995