EBMAsianOptions           package:fOptions           R Documentation

_E_x_p_o_n_e_n_t_i_a_l _B_r_o_w_n_i_a_n _M_o_t_i_o_n _D_i_s_t_r_i_b_u_t_i_o_n_s

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

     A collection and description of functions  used in the theory of
     exponential Brownian  Motion and in the valuation of Asian
     options. 

     The functions for Moment matching and Series Expansions are:

       'MomentMatchedAsianOption'   Valuate moment matched option prices,
       '... method="LN"'            Log-Normal Approximation of Levy, Turnbull and Wakeman,
       '... method="RG"'            Reciprocal-Gamma Approximation of Milevski and Posner,
       '... method="JI"'            Johnson Type I Approximation of Posner and Milevsky,
       'MomentMatchedAsianDensity'  Valuate moment matched option densities,
       '... method="LN"'            Log-Normal Approximation,
       '... method="RG"'            Reciprocal-Gamma Approximation,
       '... method="JI"'            Johnson Type I Approximation,
       'GramCharlierAsianOption'    Calculate Gram-Charlier option prices.

       'AsianOptionMoments'  Methods to calculate Asian Moments,
       '... method="A"'      Moments from Abrahamson's Formula,
       '... method="D"'      Moments from Dufresne's Formula,
       '... method="TW"'     First 2 Moments from Turnbull-Wakeman,
       '... method="T"'      Asymptotic Behavior after Tolmatz.

       'ZhangAsianOption'  Asian option price by Zhang's 1D PDE,
       'VecerAsianOption'  Asian option price by Vecer's 1D PDE.

       'gGemanYor'            Function to be Laplace inverted,
       'GemanYorAsianOption'  Asian option price by Laplace Inversion,
       'gLinetzky'            Function to be integrated,
       'LinetzkyAsianOption'  Asian option price by Spectral Expansion.

       'BoundsOnAsianOption'          Lower and upper bonds on Asian calls,
       'CurranThompsonAsianOption'    From Thompson's continuous limit,
       'RogerShiThompsonAsianOption'  From Thompson's single integral formula,
       'ThompsonAsianOption'          Thompson's upper bound,
       'TolmatzAsianOption'           Lower Bound from Tolmatz' symptotics.

       'CallPutParityAsianOption'  Call-Put parity Relation,
       'WithDividendsAsianOption'  Adds dividends to Asian option formula.

       'FuMadanWangTable'    Table from Fu, Madan and Wang's paper,
       'FusaiTaglianiTable'  Table from Fusai und tagliani's paper,
       'GemanTable'          Table from Geman's paper,
       'LinetzkyTable'       Table from Linetzky's paper,
       'ZhangTable'          Table from Zhang's paper,
       'ZhangLongTable'      Long Table from Zhang's paper,
       'ZhangShortTable'     Short Table from Zhang's paper.

     Sorry - The Documentation is still Uncomplete.

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

     MomentMatchedAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
         r = 0.09, sigma = 0.30, table = NA, method = c("LN", "RG", "JI"))
     MomentMatchedAsianDensity(x, Time = 1, r = 0.09, sigma = 0.30, 
         method = c("LN", "RG", "JI"))
     GramCharlierAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
         r = 0.09, sigma = 0.30, table = NA, method = c("LN", "RG", "JI"))

     AsianOptionMoments(M = 4, Time = 1, r = 0.045, sigma = 0.30, log = FALSE, 
         method = c("A", "D", "TW", "T"))

     ZhangAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
         r = 0.09, sigma = 0.30, table = NA, correction = TRUE, nint = 800, 
         eps = 1.0e-8, dt = 1.0e-10)
     VecerAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
         r = 0.09, sigma = 0.30, table = NA, nint = 800, eps = 1.0e-8, 
         dt = 1.0e-10)  

     gGemanYor(lambda, S = 100, X = 100, Time = 1, r = 0.05, sigma = 0.30, 
         log = FALSE, doplot = FALSE)
     GemanYorAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
         r = 0.09, sigma = 0.30, doprint = FALSE)
     gLinetzky(x, y, tau, nu, ip = 0)
     LinetzkyAsianOption(TypeFlag = c("c", "p"), S = 2, X = 2, Time = 1, 
         r = 0.02, sigma = 0.1, table = NA, lower = 0, upper = 100, 
         method = "adaptive", subdivisions = 100, ip = 0, doprint = TRUE, 
         doplot = TRUE, ...)

     BoundsOnAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
         r = 0.09, sigma = 0.30, table = NA, method = c("CT", "RST", "T"))
     CurranThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, 
         Time = 1, r = 0.09, sigma = 0.30)
     RogerShiThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, 
         Time = 1, r = 0.09, sigma = 0.30)   
     ThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
         r = 0.09, sigma = 0.30)
     TolmatzAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
         r = 0.09, sigma = 0.30)

     CallPutParityAsianOption(TypeFlag = "p", Price = 8.828759, S = 100, 
         X = 100, Time = 1, r = 0.09, sigma = 0.3, table = NA)
     WithDividendsAsianOption(TypeFlag = "c", Dividends = 0.45, S = 100, 
         X = 100, Time = 1, r = 0.09, sigma = 0.3, 
         calculator = MomentMatchedAsianOption, method = "LN")

     FuMadanWangTable()
     FusaiTaglianiTable()
     GemanTable()
     LinetzkyTable()
     ZhangTable()
     ZhangLongTable()
     ZhangShortTable()

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

calculator: [*] - 
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correction: [*] - 
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Dividends: [*] - 
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  doplot: [*] - 
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 doprint: [*] - 
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      dt: [*] - 
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     eps: [*] - 
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      ip: [*] - 
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  lambda: [*] - 
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     log: [*] - 
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   lower: [*] - 
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       M: [*] - 
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  method: [*] - 
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    nint: [*] - 
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      nu: [*] - 
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   Price: [*] - 
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       r: [*] - 
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       S: [*] - 
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   sigma: [*] - 
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subdivisions: [*] - 
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   table: [*] - 
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     tau: [*] - 
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    Time: [*] - 
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TypeFlag: [*] - 
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   upper: [*] - 
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       x: [*] - 
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       X: [*] - 
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       y: [*] - 
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     ...: [*] - 
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_A_u_t_h_o_r(_s):

     Diethelm Wuertz for the Rmetrics R-port.

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

     ## SOURCE("fOptions.3E-EBMAsianOptions")

     ## Examples:
        # none ...

