Castagna Antonio FX Options And Smile Risk

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.e., the 21st in this case)." The trade date is 19 October 2007.From the market calendars the spot settlement date forsuch a trade date is 24 October, thus the option s settlement date is 24 November, which isa Saturday, so it is shifted forward to the first available business day for both currencies:Monday 26 November.Working backward to calculate the expiry date, we would take 22November but this is a US holiday, so we move one more day backward and set the expiryon the 21st, which agrees with spot settlement rules.After analysing the rules for standard expiries, for the sake of completeness we just remarkthat if a specific date is agreed upon for the expiry (e.g., 7 January 2008), then the standardspot settlement rules apply to calculate the option s settlement date (9 January, if the contract spair is EURUSD).1.3.3 PremiumThe option s premium is paid on the spot settlement date corresponding to the trade date.Itcan be paid in one of either currencies of the underlying pair and it can be expressed in fourdifferent ways, which we list below:1.Numeraire currency units ( pnumccy ).This is the standard way in which, for some pairs,premiums are expressed for plain vanilla options in the interbank market after the closingof the deal.It is worth noticing also that this is the natural premium one calculates by apricing formula.The actual premium to pay is calculated by multiplying the currency unitstimes the notional amount (in base currency units): N � pnumccy.2.Numeraire currency percentage ( pnumeccy%).This is the standard way in which premiums areexpressed and quoted for exotic (one-touch, double-no-touch, etc.) options in the interbankmarket, when the payout is a numeraire currency amount.It can be calculated by dividingpnumccythe premium in numeraire currency units by the strike: pnumccy% = � 100.The actualKpremium to pay is equal to the notional amount in numeraire currency units (N � K ) timespnumccy%the numeraire currency percentage premium: Nnumccy �.1003.Base currency units ( pbaseccy ).This way of quoting may be useful when the numerairecurrency amount is fixed for all the options entering into a given strategy (e.g., in an EURcall USD put spread).It can be calculated by dividing the premium in numeraire currencypnumccyunits by the spot FX rate and then by the strike: pbaseccy =.The actual premiumSt Kto pay is equal to the notional amount, expressed in numeraire currency (that is: N � K ),times the base currency units premium: Nnumccy � pbaseccy.4.Base currency percentage ( pbaseccy%).This is the standard way in which premiums areexpressed and quoted for exotic (barrier) options, and for some pairs also for plain vanillaoptions, in the interbank market.It can be calculated by dividing the premium in numerairepnumccycurrency units by the spot FX rate: pbaseccy% = � 100.The actual premium to payStpbaseccy%is equal to the notional amount times the base currency percentage premium: N �.100In Table 1.3 we report some market conventions for option premiums; usually, the numerairecurrency premium is multiplied by a factor such that it is expressed in terms of pips (see abovefor the definition of the latter), or as a percentage of either notional rounded to the nearestquarter of 0.01%.We will see later that the way markets quote premiums has an impact on thebuilding of the volatility matrix, so that it is not just a curiosity one may lightly neglect.14 FX Options and Smile RiskTable 1.3 Market conventions for option premiums for some pairsPair pnumccy pbaseccy %EURUSD USD pipsEURCAD CAD pipsEURCHF EUR %EURGBP GBP pipsEURJPY EUR %EURZAR EUR %GBPCHF GBP %GBPJPY GBP %GBPUSD USD pipsUSDCAD USD %USDCHF USD %USDJPY USD %USDZAR USD %Example 1.3.2.Assume we want to buy 2 000 000 EUR call USD put struck at 1.3500, witha reference EURUSD spot rate equal to 1.2800.The notional amount in USD is 2 000 000 �1.3500 = 2 700 000.The premium can be quoted in one of the four ways we have examinedand we have that:1.If the premium is in numeraire currency units and it is pUSD = 0.0075 US dollars per oneEUR unit of option, we will pay 2 000 000 � 0.0075 = 15 000 USD.2.If the quotation is expressed as a numeraire currency percentage, the premium is pUSD% =0.0075� 100 = 0.5550% (rounded to the nearest quarter of 0.01%) for one USD unit of1.3500option dollar, and we pay 0.5550 � 2 700 000 = 14 985 USD (the small difference of 15 000100is due to rounding conventions).753.If the quotation is in base currency units, the premium is pEU R = = 0.004351.2800�1.3500EUR per one USD unit of option dollar, and we pay 0.55 � 2 700 000 = 11 750 EUR.1000.00754.Finally, if the premium is expressed as a base currency percentage, it is pEU R% = �1.2800100 = 0.5875% of the EUR notional (rounded to the nearest quarter of 0.01%) and we pay2000 0000.5875 = 11 750 EUR.1001.3 [ Pobierz całość w formacie PDF ]

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