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 US  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:

       'FEInDomesticFXOption'  Foreign Exchange In Domestic Currency Option,
       'QuantoOption'          Quanto Option,
       'EquityLinkedFXOption'  Equity Linked FX Option,
       '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)

