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L�Q$ïHvA–™h•!ÿ!à$£È™vâ€5ˆ3(’€Vµ’ÀÅœ‚‰yæLD$o·Í\ŽXå¶MCS5ê}„ 8úaÁyOs:IJjgÈ(�QàDP Û§ä.g¼³ît)gºŽ­H2�`,p¡( ”'fhµ0Ë^˜{01KâdegÈ(�Q £@F��ˆý Ðs©ì0¥îÍÀÄ”™“Q £@F�ŒN*2¶ÿIíù¬Ý2 dÈ(�Q`Jøÿ ƒ7ÎU7QIEND®B`‚èÐ@é(€àà€ ò/È 0ÒÕL·DArial¨¹¨¹XI¤(¸¸ç0(¸z[ 0 ¸¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ lðdðØdL     ð,bð$u¥9Ð u…YûŒ:ò¶Dÿ6ƒ ð0�ƒ†A¿ÀÅAÿ@ñ÷ðó€Ðwº“°öÊš;­”ÇÊš;úgþý4VdVd@¸z[ 0²ÿÿÿ”ÿÿÿpûppû@ <ý4ddddl¸ß 0¨¹0I¤ÿ <ý4BdBdl¸¾< 0¨¹ˆ8Š0º___PPT10‹ pµpµ?ÙˆÚ% ºtNasir Afaf, CQF Lecture, April 2007 - update ICBI May 2008OÙ Ú =ð¹;óŸ¨ NON-LINEAR WORLD LINEAR MODELS?¡,!,,Ÿ¨d Nasir Afaf Disclaimer: The views expressed here are those of the author and not Commerzbank AG¡DPVP VªV óŸ¨Pyramid of Modern Finance ¡Ÿª óŸ¨ Real MarketsŸ¨ŠDifferent classes of market participants Characterised by different End objectives Time horizons Risk appetite Response to market dynamics¡&DGDGª) UóŸ¨Market ParticipantsŸ TCorporates  hedgers Market making institutions Investors: Hedge funds/Proprietary Trading Desks Real money managers  asset managers, pension funds etc CTA s Retail ¡&;p;pª$ � óŸ¨Market Participants Behaviourª Ÿ¨zEquity Smile Example Equity Skew for downside is systematic risk premium for investors holding primarily long positions. Equity Sell off would trigger stop losses, and a quick down move. Therefore premium for downside puts Skew stays bid for downside even if equity markets trend upward, so not a statistical predictor of future moves, rather a descriptor of pain thresholds ¡@ZfZSóŸ¨Market Participants Behaviourª Ÿ ÄFX  Carry Smile example  Carry traders look to earn higher yield through borrowing in low interest rate economies and depositing in higher interest rate economies. Example EUR/TRY, with a 1y rate differential of 15% (1500bp)  Carry traders carry risk that the higher yielding currency weakens  therefore risk reversals (skew) systematically bid for strong currency calls (puts on the higher yielding currency) As systematic as Equity Skew. USD/JPY is the biggest example ¡JZÄZZZÊó Ÿ¨Market Participants Behaviourª Ÿ rEquity and FX Skew Direction Comparison On a statistical examination Equity and FX markets appear very different. Opposite directions of skew as compared to Forward points. But misleading. Understanding of both markets shows that same dynamics give rise to opposing skews. Both markets willing to pay a premium for getting out of their long positions Equity investors look to make money through capital appreciation from long equity positions. Their  pain is a sell off in equities  hence willing to pay for downside protection. FX investors look to make money through  carry . Their  pain is a weakening of the higher yielding currency  hence willing to pay for upside protection. ¡z(ZŒZZZ(HO¢Xó Ÿ LMarkets are non-linear  the weak part¡''Ÿ ÚInteraction amongst market participants is key. He (unknown) did this, so I do that& .. To understand how that interaction occurs you have to understand each type of participant. For example, asset managers do not adjust their holdings frequently. Certain types of hedge funds may do ( Renaissance ?) This gives rise to price dynamics in short term. ¡n_ V ó Ÿ PMarkets are non-linear  the strong part¡))Ÿ¨2Interaction is played out against a backdrop of liquidity, credit lines, levels of permitted risk, introduction of new financial instruments This generates price dynamics. Perfectly random to a pure statistician with no insight into what constitutes a market. Structured randomness for an insightful market participant. Information and insight is the key. Resulting price dynamics strongly feed back into liquidity, credit lines, levels of permitted risk, introduction of new financial instruments. This never ending feedback loop is what we call a market. ¡’0ZZ 7 &j3ó  Ÿ¨Using Derivatives ModelsŸ Model first, or think first Linear SDE etc& Linear models highly idealised  though useful. Easiest to model. Real pricing is non-linear. Price can never be independent of risk limits, and the risk in your book. You always have to make mental adjustments. ¡< ªA Æó  Ÿ¨So who is a Derivatives TraderŸ¨\Linear model Non-linear markets with feedback effects Non-linear pricing with respect to mental adjustments to account for risk in book, and risk limits etc A derivatives trader is a non-linear control hired by the bank to trade non linear instruments valued using linear models. This non-linear control is generally far from optimal! ¡VQ�-‡ ó Ÿ¨!Ingredients in non-linear controlŸ Specific Mkt risk limits Credit limits Performance year to date! Current book profile Availability (and understanding!) of  useful models ¡< ‚ ‚ª ó Ÿ¨!Ingredients in non-linear controlŸ General (Market Specific) Regulatory framework Liquidity (Depth of market) Transaction costs Aggregate  market maker positioning ¡HhióŸ¨Missing ingredient in modelsŸ¨ALiquidity Derivatives Models assume an infinite sea of liquidity Economic concepts of liquidity? My concept of liquidity: All price changes are due to the ebb and flow of liquidity. It is only meaningful to speak of liquidity at a certain price level and at a certain time. Every price movement is a liquidity squeeze. ¡t Z7ZZ W:ŠóŸ¨Feedback effectsŸ ÞFeedback Derivatives Models ( no arbitrage ) valuations are based on hedging recipes Superiority of a model based on how well  recipe can be executed in practise Can divide products/models into different classes. Easy to hedge recipe ( fwd ), difficult to hedge recipe ( short date digital ). Market risk aggregation due to popularity of products/ideas/structures. ¡8 ZfZZ gªšÎóŸ dFeedback from derivatives  recipes into liquidityŸ XPyramid of modern finance (slide 1). Not so one way! Each popular product creates its own feedback Ever changing nature of liquidity, creates new opportunities, and more products Sometimes best way to trade cash is to be on top of complex exotics ( know the top of the pyramid, trade the base ) ¡f(ZZZZZ(óŸ¨Modeling liquidity - 1Ÿ <Tangible Inputs Tangibles (available to all) Bid-offer spreads in market Volatility levels and other such information  Sea of all available market data  Theory of everything model or specific  phenomenological model from observable market data. Trade-offs between model choices. ¡pîî óŸ¨Modeling liquidity - 2Ÿ JIntangibles Effective  information set and analysis Modelling  interaction Modelling non-linear feedback Distinction between market-makers and market takers. Claim: over emphasised. Market makers are often market takers.  Inventory management is best analogy for market making activity. ¡2  ª>5  W oóŸ¨Successful liquidity modellingª Ÿ <Any reasonable liquidity model (understanding) must be dynamic rather than static. Be able to explain some phenomenon not amenable to traditional approaches ( wisdom rather than  proof ) Must then imply a dynamical statement for price dynamics  and produce observed  statistical signatures As in  chess feedback and adaptive responses, tactical and strategic, must appear. These are subjective ingredients. ¡<œPPPœóŸ¨What it comes down toŸ XDerivatives valuations cannot be expected to be unique. Different  information set , different  subjective analysis of interaction , different  strategy , for each participant is key. Traders attempt to  control this non-linearity heuristically. At least the thoughtful (successful?) ones do! ¡8*ZZZ*óŸ FWhat it comes down to  BIG PICTUREŸ ,All comes down to  predicting and modeling Order Flow. 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