Under such regulatory pressure, innovation is the key to better response to the challenge post Lehman default.

In fact, innovation has always be a key component of the financial industry, but it is not anymore about how to maximise the profit but how to handle risk which include identifying, quantifying and reducing our exposure.

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Margin and Exotic Collateral Agreement


After the Euro crisis, regulators have pressured financial institutions for more capital reserve. In this context, the industry felt pushed to collateralise. ”collateralise or dye!” Margining is not a simple process, it needs effort and has a clear cost. For instance hedge fund can not afford the margin call liquidity and operational cost of collateral management. After the crisis some institutions where still trading in the OTC market without any charges (shadow banking) but soon the regulators pushed for margining or exposition management. In order to respond to these constraints, institutions consider explicit exotic cash account margining process associated to a transaction(included in the termsheet). In this article we will focus on those without any margin call period. We will first present the computational issue then proposed a solution from the naive to the complex. In the last section, we present numerical results concerning our quantitative impact analysis.



Nothing is Clear About the Clearing



The rationale behind clearing in financial markets is twofold: clearing houses are aimed at reducing the vulnerability to systemic risks and at changing the allocation of default risk in financial markets and, thus, improve the efficiency of financial markets. This paper mitigates the standard idea according to which clearing reduces systemic risk and promotes market efficiency. The visibility associated to the clearing system will have a cost that most regulators are not ready to face.


Liquidation Process and Swing option


After the default of Lehman Brother, the credit risk became a first concern. Following the Euro crisis, the regulators were pushy for clearing i.e. the market participants were forced via the regulatory capital constraints to go to the exchange or the central clearing house. It was the beginning of the end of the Over The Counter(OTC) derivatives. Many authors warned about the fact that the OTC is a necessary complement of the Exchange system. Indeed, these decisions impose a need for liquidity which will be in favor of few participants. Kamtchueng did a note concerning the parallel with the Repo market. It will create a clear monopole, end of innovation and any introduction to new market participants. Therefore the freezing market will be driven by few participants without need of risk appetite but more willing to find a profitable consensus(comparable to the French Telecom Operators agreement condemned in 2005). Nevertheless it is important to understand(and not underestimate) the liquidation processus. The clearing process has been described in Kamtchueng(2015), you will be focus on the collateral account liquidation process and the link to the Swing Option.

Our results are also related to risk management or liquidator agent intervention, indeed the way the portfolio is liquidated will impact the final position value. As a reminder the Societe General management board decided to liquidate J.Kerviel position on 3 days(from the January 21 2008) with the dominant agent position against them. On the risk side, we also can challenge the number of liquidation days proposed by the regulators. Effectively our PFE can be at a scenario no liquidable on δ days.



Collateral and PDE’s


After Lehman default (credit crisis 2007), practitioners considered the default risk as a major risk. The regulators pushed the industry to use collateral in order to reduce the risk. Kamtchueng shown that the procedure is more a share of default risk against a funding cost. In this new world, we want to see how this new considerations affect the theory related to the partial differential equation pricing methodology. First, we consider a theoretical framework, which compares the collateralised portfolio to a Future contract. Then by relaxing some pre-Lehman default assumptions, we establish practical derivations. The main idea is to be able recover risk metrics associated to the margining process such as Independent Amount.



Forward Repo and Implied CVA Option


The Repurchase Agreement (called ’REPO’) is one of the most basic transaction. Indeed it could be summarized to a collateralised loan. The market of security lending and repo market is huge, more than 10 times the uncollaterised lending market. Because of funding and asset return optimisation, the quantitative effort concerning this transaction increased over the past decade . If the cash flows are simple, the contract paper is more delicate to handle! In fact, after Lehman Defaulted, the industry reconsidered the basics; meaning of the risk free rate and what is the most practical suitable rate candidate?

Under a default Fear World, the discounting was problematic, the industry has to deal with credit and liquidity risk linked to each index rate. Every basis of the ’Pre-Lehman theory was questionable. The major comment was regarding the completeness of the market.



Autocallable and Exposure:


An Autocallable is a structure which gives exotic coupon to the buyer usually indexed to a risky asset, the pricing of this structured product is not a real challenge in terms of its payoff.

If difficulties occur concerning the digital American risk, we would be focus on the exposure related to the structure. Indeed in this new world of Fear (see The Fear Pricing Theory: Credit and Liquidity Adjustment), the exposure is an essential risk metric used in order to quantify the CVA (hedging and regulatory) but also FVA (collateralised trade).

The autocallable premium is not a Markov process, indeed it is a paths dependent option giving coupon indexed on a risky asset St and depending of a trigger event function of Xt usually an accrual variable which bound the seller gain.

In this article, we establish different methodologies in

order to quantify the autocallable exposure.



Incomplete Market and Information Relevance Response to the No believer on Self Financing Replication Strategy


Black and Scholes is an institution in quantitative finance. The main innovation was in the existence of a self financing portfolio which is able to replicate the (supposedly smooth) price process of a contingent claim.

Clearly established as representation model via the market implied volatility, it is simplistic enough to understand the notion of dynamic hedging but also complex enough to capture the main risk drivers. Some assumptions are unrealistic such as the deterministic volatility of the underlying but one part of the industry rejects particularly the PDE method because of its mathematically incorrect derivation. What is wrong with this numerical method, as the Theory Pre Lehman should be independent of the numerical choice? Where is the confusion or missing points concerning the theory?

We will first derive the PDE and then respond to Gikhman comments. Then we will highlight new context which can in some degrees give reason to the skepticism thank to the new development in Information Relevance.



FVA, the Fake Debate: Why Are They  Still Debating?


Funding Valuation Adjustment (FVA) has been introduced as the CVA and DVA after the default of Lehman Brother. After the subprime crisis, the basis spread was not negligible anymore, credit and liquidity risk became the first concern. In addition, regulators put in place reforms, which associate capital reserve for each of these new risks. It became natural to adjust the so called fair premium (price associated to risk neutral measure).

In fact the debate is still opened, the industry is divided concerning its definition and its price adjustment status. The risk is real, academicians can argue but the fact is that default occur and occurred because of liquidity issues (in fact credit and liquidity are very linked to each other, as demonstrated in The Fear Pricing Theory: Credit and Liquidity Adjustment).

In one hand, we have for non cleared trade a risk associated to unknown (risky) cashflow, in the other hand we have to answer to the margin call.



FVA Modelling and Netting Arbitrage


After Lehman default and the Euro Crisis (crisis which started mid-2007), the industry started to consider the funding risk as a major risk. The practitioners began to charge for their funding cost. In this stressed context, the FVA has been the subject of intense debate, even its definition is not well established. In this article we follow the footsteps of Kamtchueng by establishing netting arbitrage in the FVA framework relative to our hedging strategy. It is the first time that the FVA is related to another funding spread.



Rogue Trading or Directional Hedging? Information Relevance Theory


The definition seems clear.

« A rogue trader is an employee authorised to make trades on behalf of his employer (subject to certain conditions) who makes unauthorised trades. »

But what does mean « subject to certain conditions »? In this paper, we tried to find a mathematical ground able to explain directional decision. We extend the previous work on Information Relevance of Kamtchueng to give some intuitive and quantitative explanation of trader decision. Indeed under this new theory, we suppose that each Agent has his own Information.

In this article, we explain some trading mechanisms and let the reader defined by himself the real definition of a Rogue Trader.

We consider an Agent, A (which can be J. Kerviel or K. Adoboli for instance), and his trading view on a stock, how can he make money of his vision. What are the consequences of his directional position under different risk management and risk appetite context?



SPM Extension


In this paper, we proposed to present a no-academic model , the SPM, which perform a good ‘perfect’ calibration of the smile. Between the Black and Scholes and the Local Vol, the SPM was developed a decade ago. In the first part, we present the classic implementation then in a second part we introduce some extensions; one reflecting the correlation skew and an other one implying a temporal copula fitting via the OTC market.



‘Very’ long Step Local Volatility


After 1987 crash, the financial industry has to react to the ’new’ smile phenomena. The

Black and Scholes assumption of constant volatility was not valid, therefore market participants started to innovate models which take into account the entire market volatility surface. One famous and former market standard is the local volatility model. Usually attributed to Dupire (the industry considers also the works of Derman), the local volatility is defined as the unique Markovian volatility fitting the market. The assumptions are strong and quiet disparate from the reality. The Stochastic Differential Equation (SDE) describing the stock implied small time steps, in addition the local volatility is dependent of a non ’real’ continuum of call. Reghai described the notion of Most Likely Path in order to produce another local volatility surface (based on less strong assumptions). In this article, we develop framework to implement this model with long time steps. In order to respond to multiple market challenges linked to derivative pricing and risk management.



Autocallable More American than European?


The Autocallable is a strutured product which involves payment of more or less exotic coupons until a callable event. The Digital risk at each coupon payment date induces hedge difficulties. Indeed, closer to the trigger event, the trader faces hedging difficulties at each fixing between the potential rebate and the future value of the option (which maybe very different



Fear Pricing Theory: New  Pricing PDE’s


After Lehman defaulted (credit crisis which started in 2007), the industry woke up within a new world where nobody is too big to fail. Many adjustments have to be made to the old – classic theory. As a result of the market incompleteness, the risk neutral measure became a risk neutral measure. As shown in « CVA, DVA, FVA, LVA, CSA and What else? », the price is related to the seller-buyer identities.

In order to illustrate the industry evolution, we will study the new pricing PDE’s and the assumption used to establish them.



CVA,  Premium  or Charge? CVA Call Hedging


After Lehman collapse, Market participants started to consider the credit risk as a major risk. It become vital to charge the potential default of the counterparty at the trading level. The CVA became rapidly a standar when two institutions want to trade a derivative product. The main task of this paper is to determine an efficient hedging strategy of a simple CVA call. We first try to clarify the trading meaning of the CVA; is it a premium? if yes of what type of option? is it a credit risk measure? if yes what is the meaning of trading CVA? This paper can be seen as a complement of the CVA Implied Vol and Netting Arbitrage.




CVA Implied Vol Netting Arbitrage


After Lehman default (credit crisis which started in 2007), practitioners considered the default risk as a major risk. The Industry began to charge for the default risk of any derivatives. In this article we try to extend the work of V.Piterbarg who established the fundamental of a new world in the pricing of derivatives. Our main focus will be on the Equity CVA but can be extended to any asset class. In this article we established the default risky price of particular space of derivatives based on vanilla CVA then we introduced the CVA implied Volatility and described a new pricing methodology.