Impacts of the New Pricing Paradigm on the Life of an Option Trader

1. Impacts of the New Pricing Paradigm on the Life of an Option Trader London - September 2013

2. Modelling Derivatives • In finance there is no such thing as an experiment • Model Risk / Model Uncertainty

3. Why / When should we change the model? In Physics  There is a Supreme court (experiments). In Finance / Economy (no way to test).

4. Why / When should we change the model? • A Crisis can be a period of model change. • Sometimes a change is necessary but sometimes it is just motivated by a “witch hunt” after a crisis. • We will see 2 examples that illustrate both things.

5. Why / When should we change the model? • If a central bank apply a mathematical model to adjust some macro-economical parameters in order to prevent a crisis, the time just after a crisis is probably a good moment to change the model(DSGE). • If we have a model to price a derivative contract (model that we know to be just an approximation of the reality). We should be clever in our post crisis analysis and at least take a breather before considering the model as responsible of the crisis. (Gaussian copula, CDO). • If we have a model that is a sufficient approximation at a given moment but become suddenly insufficient (after a crisis). We should estimate the gap and change the model if necessary(like for example IRS: 2 curves valuation – more than a model it is a “procedure”, or also CVA DVA terms).

6. Why / When should we change the model? Like a brief introduction to the “model changing” topic let just glance through the two first examples mentioned on the previous slide

7. Economy: A Model to Prevent from Depression

8. DSGE • Imagine a Mathematical Model use to know on which macroeconomic parametres one should act in order to stabilise the global economy and prevent it from a crisis. • Dynamic Stochastic General Equilibrium (DSGE)

9. DSGE • Applied general equilibrium model. Considered more scientific than earlier models since it is based on micro-economic foundations. • Central problem of depression-prevention has been solved. (Like Lord Kelvin in 1900).

10. DSGE • Uniqueness • Stability of the equilibrium • More generally : conformity with reality. (imitation, interdependence, contagion, interaction, trust, networks,…). • The aggregate behaviour of large systems of interactive individuals, molecules, or particles, which are widely studied in other fields, is not typically that of an average or representative member of the population. • If we stick to the physical analogy there is no warning that the system will go through a phase transition. A system may switch rapidly from one phase to another depending on its internal organization and not on some major exogenous shock.

11. DSGE

12. DSGE • The crisis is a story of contagion, interdependence, interaction, networks, and trust.

13. Gaussian Copula

14. Gaussian Copula • Derivatives : witch hunt. • You should never confuse Model & Reality. Lot of mathematicians have advise long before the crisis. • There are still people thinking that a formula killed Wall Street. (That paper is not even wrong enough to be interesting).

15. Gaussian Copula • Is the crisis due to poor modelling? • If you have an excellent and complete model to explain asset correlation but you calibrate it assuming housing prices won’t fall, the model cannot hedge you (GIGO).

16. Gaussian Copula • Mathematics become a bad word (in spite of numerous pre crisis warnings). • Come back to the source : Henri Poincaré gave the first warning to Bachelier (Efficient Market).

17. Interest Rate Swap

18. IRS • After the “explosion” of the basis gap between the different libor/euribor we had a period of time during which nobody agreed about the price of a simple plain vanilla swap. • “This is nothing else that a new equilibrium configuration determined by the pressure of the increased illiquidity force, that enlarges well known effects historically very small and traditionally neglected”. Brigo.

19. IRS • Before the credit crunch (2007) interest rates quotes in the market in a consistent way. • Consistencies between rates  construction of well defined zero coupon curve (bootstrapping+interpolation). • August 2007: the liquidity crisis widened the basis. • Market rates that were consistent with each other suddenly revealed a degree of incompatibility that worsened with time (ex. Fwd from depo / quoted FRA). • Can this divergence create an arbitrage?

20. IRS • Divergence between FRA rates & Fwd rates implied by deposits: Arbitrage opportunity?

21. Arbitrage

22. IRS • No Arbitrage  this is about credit & liquidity issues. • Consistent construction of a yield curve  credit & liquidity theory that justify different rates at the same tenor.

23. Short End Curve Calibration • This divergence was a problem for a swap trader because of the discrepancies that it produce between very short fwd rate & euribor fixing. (synthetic rate / dynamic calibration).

24. IRS • At that moment, waiting for credit-liquidity theory to be produce, practitioners adopted an empirical approach: as many curves as underlying rates (1M, 3M, 6M, 1Y). • Futures cash-flows  underlying associated curve. • Discount  another curve. • In absence of counterparty risk or collateralized derivatives, the best proxy for a classic risk-neutral curve is the OIS swap curve.

25. OIS Dicounting • The fact that the Forwarding Curve is now different from the Discounting Curve have consequences. • New Price procedure: • Build Discounting Curve (using preferred method). • Build multiple separated Forwarding Curves (1M, 3M, 6M, 1Y). • Compute fwd rate & cash flows • Compute DF using Discount Curve and price the IRS. • Hedge procedure: Compute the delta sensitivity on each curve and hedge with the corresponding set of vanillas instruments.

26. Model Risk • Let’s come back to Model Risk: What can a derivative trader do in order to hedge her portfolio against P&L gap. • If the curve change the gap is not linear in an IRS portfolio but depend on the strike (ITM, ATM, OTM,…) • Interpolation Method (global methods are out of fashion). • Bootstrapping methods in the presence of 2 curves.

27. Model Risk • You have to anticipate and simulate the model change (stress tests on your portfolio). • After the crisis during a period (that period where nobody knew the price of an IRS) Less “bid/ask business” & more stress tests.

28. The FVA Debate

29. The FVA debate • Some believe an FVA should be added by dealers to uncollateralised OTC derivatives prices to reflect the cost of funding the associated hedges. • Other “traditionalist quants” believe one should not injects subjectivity into valuations and that a price should remain independent of funding costs. • Hull and White: prices are governed by the risk-neutral pricing principle, and funding costs are irrelevant.

30. The FVA debate • It is worth to mention that Burgard & Kjaer have published a paper in which they discuss the relationship of the funding cost adjustment to the balance sheet. They demonstrate two way in which the funding cost adjustment can be eliminated. • We will briefly scan the arguments of Burgard & Kjaer and the hedge they propose in order to “re-establish” the Hull-White vision of derivative pricing and we will finally analyse if that is really useful at the trading desk level.

31. The FVA debate

32. The FVA debate

33. The FVA debate

34. The FVA debate

35. Impact on Balance Sheet

36. Derivative used as Collateral • The derivative itself could be used as collateral for funding required for negative balances on the cash account, the required margin is obtained at “risk-free rate” and the FVA term is eliminated. An alternative way to eliminate FVA is the following…

37. Balance Sheet Management to mitigate Funding Costs

38. Balance Sheet Management to mitigate Funding Costs

39. Balance Sheet Management to mitigate Funding Costs

40. Conclusions • My first reaction after reading Burgard’s paper was that it is a brilliant demonstration of the fact that we definitely should include FVA in a derivative valuation. • If this is the way to replicate and hedge the funding costs we have to get it back from the client because we will no be able to implement that kind of hedge in practice. • Desks can’t just dictate when and how banks issue debt on a trade-by-trade basis.

41. Conclusions • There might be an objective risk-neutral price, but that’s theory. We are running a business and hedging it has a real cost. • In a complete market (where every claim can be perfectly hedged) there are no ambiguity and there exists a probability measure under witch a derivative can be valued as conditional expectations. • In an incomplete market there is ambiguity about all these points (measure, price, numéraire,…) and this is why funding costs should be added.

42. Conclusions • Hull says that including FVA create an arbitrage but once again, this theoretical arbitrage is a mirage.

43. Conclusions • Hull also says: “The pro-FVA people focus on the high stated interest rate and omit the savings that will occur if the bank defaults. The reason the stated interest rate is high is because the lenders expect that sometimes they will not be paid. In a risk-neutral world, the premium they receive in compensation is chosen so that, on average, the lender earns the risk-free rate – the actual cost of funds is risk-free,” he says. • This would be correct in a theoretical efficient market but in practice the market does not react instantaneously.

44. Conclusions • Price symmetry: • With just CVA & DVA both the bank and the client would agree on the price of a derivative contract. (If they use the same methodology). • With FVA the symmetry is broken.