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.Modeling Principle Scenarios should be used when a combination of prices or ratesshould be considered as a group.9.4.1 Defining How to Build a ScenarioWhere do prices come from? In some cases this can be a simple question, forinstance, when prices are published by an exchange.In other cases, partic -ularly when there are hypothetical scenarios, more complex schemes might beused.In broad terms we can see three origins of a price: publication by somebody that is widely quoted in the market, calculation from other prices ormarket characteristics, or the opinion of an individual trader or team of analysts.The first case, shown in Figure 9.18, is the most straightforward.Instructionsare required to source the relevant information.Typically these instructionscome from a source, such as Reuters, that tells where to look for information(for example, "Page 3, second column of the row starting IBM").Figure 9.18 Sourcing a scenario element.This model describes where a particular element comes from.DLKINGr[6R\O, "kΏbNvQz: www.dlking.com 192 ScenarioIn effect, using a published price makes the quote for a sourced scenarioelement derived.Rather than asserting the quote for a sourced scenario element,we derive it using the sourcing index.There is thus an argument for making thelink to a quote a derived link.This can be done safely if the link can never beasserted, as when a trader records a hunch.Asserting the quote can causeproblems because sometimes the quote can be asserted and sometimes derived.One way out of this is to use a notation for hybrid or option ally derivedrelationships (see Odell [2], page 56).This seems to take the derived issue toofar.I tend to notate according to the most common case and d escribe whathappens precisely in the supporting documentation.Example An analyst looking at prices for mail order goods can treat each company as aninformation source.The sourcing index can be a page number in a catalog.There can thenbe a separate scenario for each retailer, or an overall scenario can be built that combinesall retailers.Rather than asking for the price of an instrument, questions such as lowestprice and average price of some instrument are supported.Figure 9.18 introduces market indicator as a supertype of instrument.Thisreflects the fact that scenarios can contain things other than instruments.Forderivatives, an important part of the pricing approach is the volatility of aninstrument a number that indicates how much the value of the instrument ischanging.This volatility is not an instrument that can be traded, but it isrecorded in a scenario in the same way as an instrument.Hence a marketindicator includes volatilities, as well as all instruments.Example Foreign currency markets have many market indicators that are not instruments,including interest rates on the various currencies and the volatility of an exchangerate an indication of how much the exchange rate is changing.Example An analyst looking at prices for mail order goods is interested in the increase injeans prices.Jeans price increase becomes a market indicator but not an instrument.Jeansare both a market indicator and an instrument.Calculating scenario elements is also straightforward.The key is to acceptthat the algorithm for calculating the price can be an object in its own right.Asimple example of this is cross-rates used in foreign exchange.If we know theexchange rates for USD/DEM and for USD/GBP, then we can calculate theexchange rate for GBP/DEM as (USD/DEM) / (USD/GBP).We can representthis by having a cross-rate scenario element, which we model by having asubtype of scenario element that references other scenario elements for thenumerator and denominator of the cross-rate, as shown in Figure 9.19.Thequote for the cross-rate scenario element is then derived from the quotes for thedenominator and numerator scenario elements.Note that the denominator and numerator are expressed as scenario ele-ments rather than market indicators.If we are just expressing cross-rates asDLKINGr[6R\O, "kΏbNvQz: www.dlking.com Trading 193numeratorFigure 9.19 Calculating scenario elements by cross-rates.This can be used todetermine a third element from the ratio of two known elements.described above, then referencing the market indicators seems the most sensible(USD/GBP is a market indicator).However, the whole point of provid ingscenarios is to allow us to post several different prices, under differentassumptions, for the same market indicator.Referencing the scenario elementallows us to focus on which of these prices we are to use.There might be twoUSD/DEM figures: one from Reuters and one from LIBOR.By referencing thescenario elements, we are able to indicate which one we want.Example A trader is a specialist on the French franc.She determines the exchange ratebetween Dutch guilders (NLG) and French francs (FFR) by cross-rates using the German mark(DEM).She does this by creating a cross-rate scenario element.The market indicator for thisscenario element is NLG/FFR.For the numerator she uses the NLG/ DEM rate quoted byReuters; that is the scenario element for the instrument NLG/DEM in the Reuters scenario.However she does not get the DEM/FFR rate for the denominator from Reuters; instead sheuses her own scenario (built on the basis of her own specialized knowledge).Thus sheforms the cross-rate from scenario elements in different scenarios.The kind of approach used for cross-rates can be used for a number ofcommon calculations, where new kinds of calculations are supported by newsubtypes of the scenario element.Figure 9.20 shows a generalization of thisstructure.In this case the calculated scenario element has a list of scenarioelements as arguments and a formula.The formula represents the algorithm forthe calculation, which uses arguments provided to it by the arguments on thecalculated scenario element.For the cross-rate the formula is arg[l] / arg[2].The actual arguments are provided by the calculated scenario element.Thisallows a single formula to be reused by several calculated scenarioDLKINGr[6R\O, "kΏbNvQz: www.dlking.com 194 ScenarioFigure 9.20 A more general approach to calculated scenario elements.The formula can be a spreadsheet-style formula based on the arguments.It supports arange of arithmetic combinations of scenario element.elements.The cross-rate for GBP/DEM uses the formula with arguments, and the GBP/JPY cross-rate uses the arguments.Note the importance of providing the arguments as alist rather than the usual set for multivalued mappings.The position is essentialfor the formulas to be correctly written.Example The price change for jeans is calculated by a calculated scenario element thattakes the difference between prices of jeans in this year's scenario and last year's scenario.We can implement the formulas in several ways.One way is to hard-codeformulas in the implementation language.Since common formulas (such ascross-rates) are widely reused, hard-coding is not a disadvantage in this case.Ifthe number of formulas is small and does not change too often, this is the bestapproach
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