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option greeks in terms of underlying and base curriences

Posted: June 18th, 2012, 5:30 pm
by kremer
Hi,When I apply Black Scholes greek formulas, what is the currency of results? How should I find the results in terms of the other currency? Let say I have a plain vanilla USD Call TRY Put fx option. Spot : 1.82 TRYStrike : 1.86 TRYMaturity : 0.25 yearsRiskfreerate : %0.34Domesticrate : %8.48Volatility : %13.9then when I use BS lets say delta and gamma formulas(below)Delta = N((ln(S/K)+(Rd-Rf+V^2/2).t)/(V*sqrt(t))Gamma = N'(d1) * (1/S.V.sqrt(t))then delta is 0.51 and gamma is 3.14my first question is what is the currency of the results that is found by using these greeks? Particularly, lets say it is long 1.000.000 USD call(vs 1.860.000 TRY put), if I want to do delta hedge, should I sell 510.000 USD at the spot or should I first do some adaption to the delta value I found. If I should do modification to greek values(to find results in USD instead of TRY) what should I do? I would like to find out the greek values that I should use with 1.000.000 USD and 1.860.000 TRY.Thanks in advance

option greeks in terms of underlying and base curriences

Posted: June 18th, 2012, 6:13 pm
by daveangel
you have a call option to buy $1mm at 1.86. the delta of the option tells you how much of the USD you need to hold (in this case short) to hedge yourself. call = $1MM * f(S,K) where f(S,K) is a function that gives the price of that option per dollar.delta = dc/dS = $1mm *df/dS

option greeks in terms of underlying and base curriences

Posted: June 19th, 2012, 11:16 am
by mathmarc
QuoteOriginally posted by: kremermy first question is what is the currency of the results that is found by using these greeks? Particularly, lets say it is long 1.000.000 USD call(vs 1.860.000 TRY put), if I want to do delta hedge, should I sell 510.000 USD at the spot or should I first do some adaption to the delta value I found. If I should do modification to greek values(to find results in USD instead of TRY) what should I do? I would like to find out the greek values that I should use with 1.000.000 USD and 1.860.000 TRY.The strike 1.86 means 1.86 TRY for 1 USD. If we put that in an asset/cash description, the asset is the USD and the cash is the TRY. The present value (pv) is in the cash (TRY) and the delta is the relative quantity of asset to hold. In general the currency exposure is delta*quantity in the asset and -(delta*spot - pv)*quantity in cash. For 51% delta, to hedge the USD call you bought, you have to hold -0.51 * 1,000,000 USD and (0.51*1.82 - pv) * 1,000,000 TRY. You sell 510,000 USD in the FX transaction, receive 1,82*510,000 TRY in the FX transaction and pay pv*1,000,000 TRY as price to buy the option.