AsianOptions            package:fOptions            R Documentation

_V_a_l_u_a_t_i_o_n _o_f _A_s_i_a_n _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 Asian  options. Asian
     options are path-dependent options,  with payoffs that depend on
     the average price of the  underlying asset or the average exercise
     price.  There are two categories or types of Asian options: 
     average rate options (also known as average price  options) and
     average strike options. The payoffs  depend on the average price
     of the underlying asset  over a predetermined time period. An
     average is less  volatile than the underlying asset, therefore
     making  Asian options less expensive than standard European 
     options. Asian options are commonly used in currency  and
     commodity markets. Asian options are of interest  in markets with
     thinly traded assets. Due to the  little effect it will have on
     the option's value,  options based on an average, such as Asian
     options,  have a reduced incentive to manipulate the underlying 
     price at expiration. 

     The functions are:

       'GeometricAverageRateOption'        Geometric Average Rate Option,
       'TurnbullWakemanAsianApproxOption'  Turnbull and Wakeman's Approximation,
       'LevyAsianApproxOption'             Levy's Approximation.

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

     GeometricAverageRateOption(TypeFlag, S, X, Time, r, b, sigma)
     TurnbullWakemanAsianApproxOption(TypeFlag, S, SA, X, Time, time, tau, r, b, sigma)
     LevyAsianApproxOption(TypeFlag, S, SA, X, Time, 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. 

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

   S, SA: 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.

     tau: [TurnWakeAsianApprox*] - 
           is the time to the beginning of the average period. 

time, Time: the 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:

     The Geometric average is the nth root of the product of the n
     sample  points. The Arithmetic average is the sum of the stock
     values divided  by the number of sampling points. Although
     Geometric Asian options are  not commonly used in practice, they
     are often used as a good initial  guess for the price of
     arithmetic Asian options. This technique is  used to improve the
     convergence rate of the Monte Carlo model when  pricing arithmetic
     Asian options. 

     Two cases are considered, the geometric and the arithmetic
     average-rate  option. For the latter one can choose between three
     different kinds of  approximations: Turnbull and Wakeman's
     approximations, Levy's approximation  and Curran's approximation. 
      [Haug's Book, Chapter 2.12]

_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 2.12 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 2.12, McGraw-Hill, New York.

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

     ## Examples from Chapter 2.12 in E.G. Haug's Option Guide (1997)

     ## Geometric Average Rate Option:
        xmpOptions("\nStart: Geometric Average Rate Option > ")
        GeometricAverageRateOption(TypeFlag = "p", S = 80, X = 85, 
          Time = 0.25, r = 0.05, b = 0.08, sigma = 0.20)

     ## Turnbull Wakeman Approximation:
        xmpOptions("\nNext: Turnbull Wakeman Option > ")
        TurnbullWakemanAsianApproxOption(TypeFlag = "p", S = 90, SA = 88, 
          X = 95, Time = 0.50, time = 0.25, tau = 0.0, r = 0.07, 
          b = 0.02, sigma = 0.25)

     ## Levy Asian Approximation:   
        xmpOptions("\nNext: Levy Asian Option > ")
        LevyAsianApproxOption(TypeFlag = "c", S = 100, SA = 100, X = 105, 
          Time = 0.75, time = 0.50, r = 0.10, b = 0.05, sigma = 0.15)
          

