12.11 Currency Options Currency options trade on the Philadelphia EXchange(PHLX They are used by corporations to hedge their FX exposure The size of 1 contract depends on the currency [see Table 13.3(p 283) There also exists an active over-the-counter (OTC) market Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.11 Currency Options • Currency options trade on the Philadelphia Exchange (PHLX) • They are used by corporations to hedge their FX exposure • The size of 1 contract depends on the currency [see Table 13.3 (p. 283)] • There also exists an active over-the-counter (OTC) market
12.12 The foreign Interest rate We denote the foreign interest rate by When aU.s. company buys one unit of the foreign currency it has an investment of So dollars The return from investing at the foreign rate is r so dollars This shows that the foreign currency provides a dividend yield at rate rf Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.12 The Foreign Interest Rate • We denote the foreign interest rate by rf • When a U.S. company buys one unit of the foreign currency it has an investment of S0 dollars • The return from investing at the foreign rate is rf S0 dollars • This shows that the foreign currency provides a “dividend yield” at rate rf
12.13 Valuing european Currency Options A foreign currency is an instrument that provides a continuous income("dividend yield") foreign risk-free rate(r) We can use the formula for an option on a stock paying a continuous dividend yield Set So=current exchange rate(domestic/foreign) Set q=rt Note that the income earned in the domestic currency is rf So showing that rf is analogous to q Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.13 Valuing European Currency Options • A foreign currency is an instrument that provides a continuous income (“dividend yield” ) = foreign risk-free rate (rf ) • We can use the formula for an option on a stock paying a continuous dividend yield: – Set S0 = current exchange rate (domestic/foreign) – Set q = rf • Note that the income earned in the domestic currency is rf S0 showing that rf is analogous to q
12.14 European Options on Currency options c=Se n(di)-xe" n(d,) p=Xe N(d,)-Se/(,) Where n(S8/X)+(r-r+a2/2)T √T n(S/X)+(r-r-σ2/2)7 √7 G√T Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.14 European Options on Currency Options 0 1 2 2 0 1 e ( ) e ( ) e ( ) e ( ) f f - T -rT -r - T r T r c S N d X N d p X N d S N d = − = − − − 2 0 1 2 0 2 1 ln( / ) ( / 2) ln( / ) ( / 2) f f S X r T r d T S X r T d d T r T +−+ = +−− = = − where
12.15 Alternative formulas (Equations 12.11 and 12.12, page 284) Using FA=S c=e Fon(di-XN(d,) p=e"[XN(-d2)-FN(-d1) d=1mx)+o72 √T d1-o√T Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 12.15 Alternative Formulas (Equations 12.11 and 12.12, page 284) ( ) 0 0 f r T r F S e − Using = c e F N d XN d p e XN d F N d d F X T T d d T rT rT = − = − − − = + = − − − [ ( ) ( )] [ ( ) ( )] ln( / ) / 0 1 2 2 0 1 1 0 2 2 1 2