BasicAmericanOptions        package:fOptions        R Documentation

_V_a_l_u_a_t_i_o_n _o_f _B_a_s_i_c _A_m_e_r_i_c_a_n _O_p_t_i_o_n_s

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

     A collection and description of functions to valuate  basic
     American options. Approximative formulas for  American calls are
     given for the Roll, Geske and  Whaley Approximation, for the
     Barone-Adesi and Whaley  Approximation, and for the Bjerksund and
     Stensland  Approximation. 

     The functions are:

       'RollGeskeWhaleyOption'    Roll, Geske and Whaley Approximation,
       'BAWAmericanApproxOption'  Barone-Adesi and Whaley Approximation,
       'BSAmericanApproxOption'   Bjerksund and Stensland Approximation.

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

     RollGeskeWhaleyOption(S, X, time1, Time2, r, D, sigma) 
     BAWAmericanApproxOption(TypeFlag, S, X, Time, r, b, sigma)
     BSAmericanApproxOption(TypeFlag, S, X, Time, r, b, sigma) 

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

       b: the annualized cost-of-carry rate, a numeric value;  e.g. 0.1
          means 10% pa. 

       D: a single dividend with time to dividend payout 't1'. 

       r: the annualized rate of interest, a numeric value;  e.g. 0.25
          means 25% pa. 

       S: the asset price, a numeric value. 

   sigma: the annualized volatility of the underlying security,  a
          numeric value; e.g. 0.3 means 30% volatility pa. 

    Time: the time to maturity measured in years, a numeric value. 

time1, Time2: [RollGeskeWhaley*] -  the first value measures time to
          dividend payout in years,  e.g. 0.25 denotes a quarter, and
          the second value measures  time to maturity measured in
          years, a numeric value; e.g.  0.5 means 6 months. 

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

       X: the exercise price, a numeric value. 

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

     *Roll-Geske-Whaley Option:* 

      The function 'RollGeskeWhaleyOption' valuates American calls  on
     a stock paying a single dividend with specified time to dividend 
     payout according to the pricing formula derived by Roll, Geske and
      Whaley (1977). 

     'Approximations for American Options:'  

      The function 'BSAmericanApproxOption' valuates American calls  or
     puts on an underlying asset for a given cost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valuates Aost-of-carry rate 
     according to the quadratic approximation method due to
     Barone-Adesi  and Whaley (1987). ' valu