FXTransOptions           package:fOptions           R Documentation

_V_a_l_u_a_t_i_o_n _o_f _C_u_r_r_e_n_c_y _T_r_a_n_s_l_a_t_e_d _O_p_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

     This is a collection of functions to valuate currency translated
     options. Currency translated options are options on foreign assets
     where the  payoff is exchanged into domestic currency at
     expiration. For example,  a U.S. investor is interested in buying
     an option that is linked to  the Nikkei index that is priced in
     yen. There are two types or risks,  changing prices and exchange
     rates, to consider when valuing  currency-translated options. 

     The functions are:

       1  'FEInDomesticFXOption'  Foreign Exchange In Domestic Currency Option,
       2  'QuantoOption'          Quanto Option,
       3  'EquityLinkedFXOption'  Equity Linked FX Option,
       4  'TakeoverFXOption'      Takeover FX Option.

_U_s_a_g_e:

     FEInDomesticFXOption(TypeFlag, S, E, X, Time, r, q, 
             sigmaS, sigmaE, rho)
     QuantoOption(TypeFlag, S, Ep, X, Time, r, rf, q, sigmaS, 
             sigmaE, rho) 
     EquityLinkedFXOption(TypeFlag, E, S, X, Time, r, rf, q, 
             sigmaS, sigmaE,rho)
     TakeoverFXOption(V, B, E, X, Time, r, rf, sigmaV, sigmaE, rho)

_A_r_g_u_m_e_n_t_s:

       B: [TakeoverFX*] -  the value of the foreign firm in the foreign
          currency at  the option expiration, a numeric value. 

       E: [FEInDomesticFX*] -  the spot exchange rate specified in
          units of the domestic currency per unit of the foreign
          currency, a numeric value.
           [TakeoverFX*] - the currency price quoted in units of the
          domestic currency per unit of the foreign currency. 

      Ep: [Quanto*] - the predetermined exchange rate specified in
          units of domestic currency per unit of foreign currency. 

       q: [FEInDomesticFX*][EquityLinkedFX*] - the instantaneous
          proportional dividend payout rate of the  underlying asset, a
          numerical value. 

       r: [FEInDomesticFX*][TakeoverFX*] - the domestic interest rate,
          a numeric value. E.g. 0.25 means  25% p.a. 

      rf: [TakeoverFX*] - the foreign interest rate, a numeric value. 

     rho: [TakeoverFX*] -  the correlation between annualized
          volatility of the currency price  quoted in units of the
          domestic currency per unit of the foreign  currency and the
          annualized volatility of the value of the foreign  firm, a
          numeric value. 

       S: [FEInDomesticFX*][EquityLinkedFX*] -  the underlying asset
          price in foreign currency, a numeric  value. 

  sigmaE: [TakeoverFX*] -  the annualized volatility of the currency
          price quoted in  units of the domestic currency per unit of
          the foreign currency, a numeric value; e.g. 0.3 means 30%
          volatility pa. 

  sigmaS: [Quanto*] - the annualized volatility of the underlying
          asset, a numeric value; e.g. 0.3 means 30% volatility pa. 

  sigmaV: [TakeoverFX*] -  the annualized volatility of the value of
          the foreign firm,  a numeric value; e.g. 0.3 means 30%
          volatility pa. 

    Time: the time to maturity, a numeric value. 

TypeFlag: a character string either "c" for a call option or a "p"  for
          a put option. 

       V: [TakeoverFX*] -  the value of the foreign firm in the foreign
          currency, a  numeric value. 

       X: [FEInDomesticFX*] - the strike (delivery) price in domestic
          currency, a numeric  value. 
           [TakeoverFX*] - the strike price quoted in units of the
          domestic currency per unit of the foreign currency. 

_D_e_t_a_i_l_s:

     *Equity Linked Foreign Exchange Options:* 

      An equity-linked foreign-exchange option is an option on the
     foreign  exchange rate and is linked to the forward price of a
     stock or equity  index. This option can be priced analytically
     using a model introduced  by Reiner (1992). 

     *Quanto Options:* 

      A fixed exchange-rate foreign-equity option (Quanto) is
     denominated in  another currency than that of the underlying
     equity exposure. The face  value of the currency protection
     expands or contracts to cover changes  in the foreign currency
     value of the underlying asset. Quanto options  can be priced
     analytically using a model published by Dravid, Richardson,  and
     Sun (1993). 

     *Foreign Equity Options:* 

      A foreign equity option is an option on a foreign asset where the
     strike  price is specified in either domestic or foreign currency
     and the payoff  at expiration is valued in domestic currency.
     Foreign equity options  can be priced analytically using a model
     introduced by Reiner (1992). 

     *Takeover Foreign Exchange Options:* 

      A takeover foreign exchange call option gives the buyer the right
     purchase  a specified number of units of foreign currency at a
     strike price if the  corporate takeover is successful. This option
     can be priced analytically  using a model introduced by Schnabel
     and Wei (1994). 
      [Haug's Book, Chapter 2.13.4]

_V_a_l_u_e:

     The option price, a numeric value.

_N_o_t_e:

     The functions implement the algorithms to valuate plain vanilla 
     options as described in Chapter 1 of Haug's Book (1997).

_A_u_t_h_o_r(_s):

     Diethelm Wuertz for this R-Port.

_R_e_f_e_r_e_n_c_e_s:

     Haug E.G. (1997);  _The Complete Guide to Option Pricing
     Formulas_,  Chapter 2.13, McGraw-Hill, New York.

_E_x_a_m_p_l_e_s:

     ## Examples from Chapter 2.13 in E.G. Haug's Option Guide (1997)

     ## Foreign Equity Options Struck in Domestic Currency [2.13.1]:
        xmpOptions("\nStart: FE in Domestic Currency Option > ")
        FEInDomesticFXOption(TypeFlag = "c", S = 100, E = 1.5, 
          X = 160, Time = 0.5, r = 0.08, q = 0.05, sigmaS = 0.20, 
          sigmaE = 0.12, rho = 0.45)

     ## Fixed Exchange-Rate Foreign-Equity Option [2.13.2]: 
        xmpOptions("\nNext: Quanto Option > ")
        QuantoOption(TypeFlag = "c", S = 100, Ep = 1.5, X = 105, 
          Time = 0.5, r = 0.08, rf = 0.05, q = 0.04, sigmaS= 0.2, 
          sigmaE = 0.10, rho = 0.30) 

     ## Equity Linked Foreign Exchange Option [2.13.3]:
        xmpOptions("\nNext: Equity Linked FX Option > ")
        EquityLinkedFXOption(TypeFlag = "p", E = 1.5, S = 100, 
          X = 1.52, Time = 0.25, r = 0.08, rf = 0.05, q = 0.04, 
          sigmaS = 0.20, sigmaE = 0.12, rho = -0.40)

     ## Takeover Foreign-Exchange Option [2.13.4]:
        xmpOptions("\nNext: Takeover FX Option > ")
        TakeoverFXOption(V = 100, B = 100, E = 1.5, X = 1.55, Time = 1, 
          r = 0.08, rf = 0.06, sigmaV = 0.20, sigmaE = 0.25, rho = 0.1)

