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). The function
     'BSAmericanApproxOption' valuates  American calls or puts on
     stocks, futures, and currencies due to  the approximation method
     of Bjerksund and Stensland (1993).

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

     'RollGeskeWhaleyOption' 
      'BAWAmericanApproxOption' 
      return the option price, a numeric value. 

     'BSAmericanApproxOption' 
      returns a list with the following two elements: 'Premium' the 
     option price, and 'TriggerPrice' the trigger price.   

_N_o_t_e:

     The functions implement the algorithms to valuate basic American 
     options as described in Chapter 1.4 of Haug's Option Guide (1997).

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

     Diethelm Wuertz for this R-Port.

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

     Barone-Adesi G., Whaley R.E. (1987); _Efficient Analytic
     Approximation of American Option Values_, Journal of Finance 42,
     301-320.

     Bjerksund P., Stensland G. (1993); _Closed Form Approximation of
     American Options_, Scandinavian Journal of Management 9, 87-99.

     Geske R. (1979); _A Note on an Analytical Formula for Unprotected
     American Call Options on Stocks with known Dividends_, Journal of
     Financial Economics 7, 63-81.

     Haug E.G. (1997);  _The Complete Guide to Option Pricing
     Formulas_,  Chapter 1, McGraw-Hill, New York.

     Roll R. (1977); _An Analytic Valuation Formula for Unprotected
     American Call Options on Stocks with known Dividends_, Journal of
     Financial Economics 5, 251-258.

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

     ## All the examples are from Haug's Option Guide (1997)

     ## CHAPTER 1.4: ANALYTICAL MODELS FOR AMERICAN OPTIONS
            
     ## Roll-Geske-Whaley American Calls on Dividend Paying 
     ## Stocks [Haug 1.4.1]
        xmpOptions("\nStart: Roll-Geske-Whaley > ")
        RollGeskeWhaleyOption(S = 80, X = 82, time1 = 1/4, 
          Time2 = 1/3, r = 0.06, D = 4, sigma = 0.30)
           
     ## Barone-Adesi and Whaley Approximation for American 
     ## Options [Haug 1.4.2] vs. Black76 Option on Futures:
        xmpOptions("\nNext: BAW Approximation > ")
        BAWAmericanApproxOption(TypeFlag = "p", S = 100, 
          X = 100, Time = 0.5, r = 0.10, b = 0, sigma = 0.25)
        Black76Option(TypeFlag = "c", FT = 100, X = 100, 
          Time = 0.5, r = 0.10, sigma = 0.25)  
          
     ## Bjerksund and Stensland Approximation for American 
     ## Options:
        xmpOptions("\nNext: BS Approximation > ")
        BSAmericanApproxOption(TypeFlag = "c", S = 42, X = 40, 
          Time = 0.75, r = 0.04, b = 0.04-0.08, sigma = 0.35)

