# Can you fully hedge an option in the presence of counterparty risk?

The derivation of the Black-Scholes model assumes no counterparty risk. Does the presence of counterparty risk invalidate the argument behind the model?

EDIT: The question is about options in general, not just the exchange-traded ones. BS model is used to price FX options, or -- in a modified form known as "Black 1976" -- IR swaptions. They're (IR swaptions at least) OTC instruments and thus would not benefit from the central clearing mechanisms.

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I answered the question that you asked. Then four hours later you edited the question, adding some very specific details. If I can, I'll respond to the edits, but will do so as a separate answer. I'm not complaining, okay? It is allowed to give two answers to the same question on StackExchange sites. –  Ellie Kesselman Jan 8 '12 at 5:00
Sure, thanks a lot for your time. –  quant_dev Jan 9 '12 at 23:27
your counterparty has to REALLY be upside down for your to lose since options are most "senior" in bankruptcy court (not legal advice, i'm not a lawyer, this doesn't really exist) –  user3232 Feb 15 '13 at 5:52

## 2 Answers

Options are actually some of the least susceptible securities to the adverse impact of counterparty risk. I refer to listed options, such as those cleared through the OCC (Options Commodity Clearinghouse) in Chicago, IL. The OCC is a true central clearing counterparty (CCC) because it bears all default risk, by distributing it evenly among its members. The default risk is distributed because all members "pay in" (provide collateral), mitigating the aggregate risk exposure in the event of a member default.

What if they don't want to pay? you may ask. Members are assessed a yearly fee to belong to the clearinghouse, which maintains these funds if needed (it is called the "insolvency fund"). Furthermore, each transaction is assessed a short-term collateral tithe, until the trade clears.

I couldn't find an example chart from the OCC, but here is one for the NSCC (National Securities Clearing Corp, now Depository Trust, DTCC), which is the other major central clearing counterparty in the U.S.A. NSCC/ DTCC acts as the CCC for listed equities, mutual funds, bonds, government securities etc. The OCC acts similarly, but for options.
In the United States, true central counterparty clearing is no longer in place for all transactions. Instead of CCC, there is usually some form of separation between the clearing broker and the clearinghouse. This means that there will be multiple clearing brokers that must reconcile financial securities (shares, bonds, options etc.) and money against other clearing brokers. It also means that the clearing broker bears the risk of default on the leg of the transaction that he is servicing.

Regarding the question, the counterparty risk IS negligible as far as the risk to both parties in the transaction, the buyer and seller of the option. * If the option is listed, the clearinghouse is in place to cover any default.

In the instance of non-CCC, there are the intermediate clearing brokers as I described above. The taxpayer is never liable here (that concern was expressed in a comment to another answer). Other than a situation of complete financial collapse, the effect of counterparty risk will not be an issue for traders. The "buck stops" with the clearinghouses and the clearing brokers.

* The clearinghouse is adequately collateralized. It includes both an annual fee for members, plus a daily collateral margin based on each transaction cleared. There is also a secondary insolvency fund as back up, for coverage in the event of a catastrophic risk scenario.

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1) What about the case of MF Global? 2) What about OTC options? –  quant_dev Jan 7 '12 at 11:50
Many OTC derivatives are collaterialized daily to make the default risk minimal. It's regulated in the Credit Support Annex (CSA) of a ISDA Master Agreement. I suppose you can call that 'hedging'. –  klon Jan 7 '12 at 16:20
@klon Yes, that is what we did at NSCC! I referred to it as a short-term collateral tithe, which sounds odd. It is just as you described, daily collateralization, based on the historical volatility over the time until settlement, T+3 for equities, T+1 for gov't securities etc. The ISDA Master Agreement is an excellent suggestion and is used for (many but not all) OTC derivatives. –  Ellie Kesselman Jan 8 '12 at 5:14
Take the example of AIG, which was acting as a sort of broker of credit protection: it was long CDO protection (from monoline insurers) and short single-name protection. The monoline protection AIG purchased turned out to be illusory, and it was swamped with margin calls. If the taxpayer didn't step in, AIG would have collapsed and its counterparties who purchased single-name protection from it would be in deep trouble. Isn't it a counterexample to your claim that there would be no need for taxpayer assistance? –  quant_dev Jan 9 '12 at 23:32

Keep in mind that most futures, equity, and index options, at least, are traded on exchanges where the counterparty risk is so tiny as to be negligible.

In general, adding extra variables like this fails to invalidate the model. For example, the fact that interest rates or volatilities are not constant just ends up leading to an extended model with extra stochastic factors (and hedges) corresponding to the extra terms.

Counterparty risk is special, however, since it moves the price in opposite directions for the two entities making the trade. That is to say, if BofA is trading an in-the-money swap with Goldman, then

• B of A thinks it should get more money because the payments Goldman promised may never materialize, but
• Goldman thinks it should pay less money because the cashflows promised by BofA may never materialize.

Contrast this with the case of stochastic interest rates, where both parties can at least theoretically come to a consensus about the effect on the value of future cashflows.

In practice, for options, only one side of this conundrum is relevant. For example if Goldman is buying an option from BofA for cash upfront, then BofA has no counterparty concerns about the deal. Goldman still wants to pay less due to the credit risk of course, while from BofA's point of view the credit risk is meaningless.

The result of all this is that counterparty risk is an unavoidable error in the model. I would not go so far as to say this risk "invalidates" it. After all even the existence of quoted spreads on the underyling theoretically "invalidates" the model.

What it does mean is that trades happen only in cases where the counterparty risk is roughly the size of the option's bid/offer spread, or less. Any more risk than that and BofA will be unwilling to accept such a large haircut, and Goldman will take its business elsewhere.

A common way to reduce the risk all around is in the use of margin accounts. For example, Goldman obviously cares little about the BofA counterparty risk if the option looks valueless. If the option becomes valuable, then Goldman can demand that BofA keep some money on deposit as a guarantee they will make good on the payments. So long as any bankruptcy by BofA is sufficiently slow to evolve, the margin account updates will have grown to entirely cover the option value by the time default actually occurs.

The margin accounts are the reason exchanges are willing to let members sell options, despite the obviously greater risk of any individual member's default.

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Is it only about the lower price? What about the completeness of the hedge? You "hedge" counterparty risk by entering into another trade with another counterparty, which carries its own counterparty risk. Does the buck stop anywhere? and where? with a "too big to fail" bank backed by the taxpayer? Sovereigns are not risk-free anymore. –  quant_dev Jan 6 '12 at 22:59
While such concerns are worth considering, they do not "invalidate the argument behind the model", but rather modify how much one is willing to rely on the model when actually deciding to trade these securities. One can take this thinking to extremes like to maniacs on the zerohedge forums, but in the end, even physical gold has mainly illusory value, since there's no guarantee the rest of humanity will continue to covet it. –  Brian B Jan 9 '12 at 14:56
Oh, of course, I'm far from being a "gold bug". I don't have an issue with using BS model "with caution". I have doubts about CVA modelling -- there it is claimed that you can price counterparty risk in a risk-neutral way (ergo, hedge it). –  quant_dev Jan 9 '12 at 23:33