Elliptic Lambda Distribution and Option Pricing Model


[Up] [Top]

Documentation for package ‘ecd’ version 0.9.2.4

Help Pages

B C D E H I J K L M N P Q R S W Y

ecd-package ecd: A package for the stable lambda distribution family.

-- B --

bootstrap Bootstrap data for the Elliptic DB (ECDB)
bootstrap-method Bootstrap data for the Elliptic DB (ECDB)
bootstrap.ecdb Bootstrap data for the Elliptic DB (ECDB)

-- C --

cfqsl Stable lambda distribution
cfsl Stable lambda distribution
cfstablecnt Stable Count distribution
cfstdlap Standardized Laplace process and distribution

-- D --

dec The Elliptic Distribution
discr Discriminant of the elliptic curve y(x)
discr-method Discriminant of the elliptic curve y(x)
discr.ecd Discriminant of the elliptic curve y(x)
dlaplace0 Laplace distribution
dqsl Stable lambda distribution
dsl Stable lambda distribution
dstablecnt Stable Count distribution
dstdlap Standardized Laplace process and distribution
dstdlap_poly Standardized Laplace process and distribution

-- E --

ecd Constructor of ecd class
ecd-class The ecd class
ecd.adj2gamma Discriminant-adjusted gamma
ecd.adj_gamma Discriminant-adjusted gamma
ecd.asymp_kurtosis Compute asymptotic statistics of an ecd object
ecd.asymp_stats Compute asymptotic statistics of an ecd object
ecd.ccdf Complementary CDF of ecd
ecd.cdf CDF of ecd
ecd.cubic Generate or solve the cubic polynomial for ecd
ecd.cusp Cusp constructor of ecd class
ecd.cusp_a2r Conversion between alpha and gamma for cusp distribution
ecd.cusp_r2a Conversion between alpha and gamma for cusp distribution
ecd.cusp_std_cf The moments, characteristic function (CF), and moment generating function (MGF) of standard cusp distribution.
ecd.cusp_std_mgf The moments, characteristic function (CF), and moment generating function (MGF) of standard cusp distribution.
ecd.cusp_std_moment The moments, characteristic function (CF), and moment generating function (MGF) of standard cusp distribution.
ecd.data Read sample data
ecd.data.arr Read sample data
ecd.data.ts Read sample data
ecd.data_stats Statistics and histogram on log returns
ecd.dawson Wrapper to convert numeric to mpfr
ecd.devel Wrapper to convert numeric to mpfr
ecd.df2ts Utility to standardize timeseries from data.frame to xts
ecd.diff Utility to diff a vector of numeric or mpfr to get first derivative
ecd.erf Wrapper to convert numeric to mpfr
ecd.erfc Wrapper to convert numeric to mpfr
ecd.erfcx Wrapper to convert numeric to mpfr
ecd.erfi Wrapper to convert numeric to mpfr
ecd.erfq Quartic scaled error function
ecd.erfq_sum Quartic scaled error function
ecd.estimate_const Estimate the normalization constant for an ecd object
ecd.fit_data Sample data fit
ecd.fit_ts_conf Timeseries fitting utility
ecd.gamma Wrapper to convert numeric to mpfr
ecd.has_quantile Whether the ecd object has quantile data or not
ecd.ifelse Wrappers for ecd to maintain consistent type between mpfr and numeric
ecd.imgf Incomplete MGF of ecd
ecd.integrate Wrapper to integrate numeric and mpfr
ecd.kurt Standard deviation, variance, mean, skewness, and kurtosis of ecd
ecd.kurtosis Standard deviation, variance, mean, skewness, and kurtosis of ecd
ecd.lag Utility to shift a vector of numeric or mpfr
ecd.manage_hist_tails Manage histogram tails
ecd.max_kurtosis Utility to calculate where the maximum kurtosis is on the positive j=0 line
ecd.mcsapply Wrappers for ecd to maintain consistent type between mpfr and numeric
ecd.mean Standard deviation, variance, mean, skewness, and kurtosis of ecd
ecd.mp1 Wrapper to convert numeric to mpfr
ecd.mp2f Wrapper to convert mpfr to numeric
ecd.mpfr Wrapper to convert numeric to mpfr
ecd.mpfr_qagi Utility to integrate mpfr with infinity via qagi
ecd.mpnum Wrappers for ecd to maintain consistent type between mpfr and numeric
ecd.mppi Wrapper to convert numeric to mpfr
ecd.mu_D Incomplete MGF of ecd
ecd.ogf Option generating function of ecd
ecd.pdf Calculate the PDF of an ecd object
ecd.polar Polar constructor of ecd class
ecd.rational Utility to convert a numeric to a rational
ecd.read_csv_by_symbol Read csv file of sample data
ecd.read_symbol_conf Read conf for sample data
ecd.sapply Wrappers for ecd to maintain consistent type between mpfr and numeric
ecd.sd Standard deviation, variance, mean, skewness, and kurtosis of ecd
ecd.setup_const Integration preprocessor for an ecd object
ecd.skewness Standard deviation, variance, mean, skewness, and kurtosis of ecd
ecd.solve_cusp_asym Trigonometric solution for asymmetric cusp distribution
ecd.stats Compute statistics of an ecd object
ecd.toString String representation of ecd
ecd.ts_lag_stats Lag statistics on timeseries of log returns
ecd.uniroot Uniroot wrapper
ecd.var Standard deviation, variance, mean, skewness, and kurtosis of ecd
ecd.y0_isomorphic The analytic solution of y(0) via isomorphic mapping.
ecdattr Constructor of 'ecdattr' class for the Elliptic Database (ECDB)
ecdattr-class An S4 class to represent the 'ecdattr' row in the Elliptic Database (ECDB)
ecdattr.enrich Enrich a basic 'ecdattr' object
ecdattr.pairs Create a list of basic 'ecdattr' objects
ecdattr.pairs_polar Create a list of basic 'ecdattr' objects in polar coordinate
ecdb Constructor of ecdb class for the elliptic database
ecdb-class setClass for ecdb class
ecdb.dbSendQuery Send query to the elliptic database
ecdb.protectiveCommit Protective commit
ecdq Constructor of ecdq class
ecdq-class setClass for ecdq class
ecld Constructor of ecld class
ecld-class An S4 class to represent the lambda distribution
ecld.ccdf CDF and CCDF of ecld
ecld.cdf CDF and CCDF of ecld
ecld.cdf_gamma CDF and CCDF of ecld
ecld.cdf_integrate CDF and CCDF of ecld
ecld.const Analytic solution of the normalization constant for lambda distribution
ecld.fixed_point_atm_ki The Q operator in option pricing model
ecld.fixed_point_atm_Q_left The Q operator in option pricing model
ecld.fixed_point_atm_Q_right The Q operator in option pricing model
ecld.fixed_point_shift The Q operator in option pricing model
ecld.fixed_point_SN0_atm_ki The ATM RNO related constants and calculations in fixed point model
ecld.fixed_point_SN0_atm_ki_sd The ATM RNO related constants and calculations in fixed point model
ecld.fixed_point_SN0_lambda_skew_ratio The ATM RNO related constants and calculations in fixed point model
ecld.fixed_point_SN0_rho_sd The ATM RNO related constants and calculations in fixed point model
ecld.fixed_point_SN0_skew The ATM RNO related constants and calculations in fixed point model
ecld.from Constructor of ecld class
ecld.from_sd Constructor of ecld class
ecld.gamma Incomplete gamma function and asymptotic expansion
ecld.gamma_2F0 Incomplete gamma function and asymptotic expansion
ecld.gamma_hgeo Incomplete gamma function and asymptotic expansion
ecld.ifelse Wrappers for ecld to maintain consistent type between mpfr and numeric
ecld.imgf Incomplete moment generating function (IMGF) of ecld
ecld.imgf_gamma Incomplete moment generating function (IMGF) of ecld
ecld.imgf_integrate Incomplete moment generating function (IMGF) of ecld
ecld.imgf_quartic Incomplete moment generating function (IMGF) of ecld
ecld.imnt Incomplete moment (imnt) of ecld
ecld.imnt_integrate Incomplete moment (imnt) of ecld
ecld.imnt_sum Incomplete moment (imnt) of ecld
ecld.ivol_ogf_star Calculate implied volatility using star OGF and small sigma formula
ecld.kurt Compute statistics analytically for an ecld object
ecld.kurtosis Compute statistics analytically for an ecld object
ecld.laplace_B Analytic solution for y(x) in lambda distribution
ecld.mclapply Wrappers for ecld to maintain consistent type between mpfr and numeric
ecld.mean Compute statistics analytically for an ecld object
ecld.mgf The moments and MGF of ecld
ecld.mgf_by_sum The moments and MGF of ecld
ecld.mgf_diterm The term structure of ecld symmetric MGF
ecld.mgf_quartic The moments and MGF of ecld
ecld.mgf_term The term structure of ecld symmetric MGF
ecld.mgf_term_original The term structure of ecld symmetric MGF
ecld.mgf_trunc The term structure of ecld symmetric MGF
ecld.mgf_trunc_max_sigma The term structure of ecld symmetric MGF
ecld.moment The moments and MGF of ecld
ecld.mpnum Wrappers for ecld to maintain consistent type between mpfr and numeric
ecld.mu_D mu_D of ecld
ecld.mu_D_by_sum mu_D of ecld
ecld.mu_D_integrate mu_D of ecld
ecld.mu_D_quartic mu_D of ecld
ecld.ogf Option generating function (OGF) of ecld
ecld.ogf_gamma Option generating function (OGF) of ecld
ecld.ogf_imnt_sum Option generating function (OGF) of ecld
ecld.ogf_integrate Option generating function (OGF) of ecld
ecld.ogf_log_slope Option generating function (OGF) of ecld
ecld.ogf_quartic Option generating function (OGF) of ecld
ecld.ogf_star Star OGF of ecld
ecld.ogf_star_analytic Star OGF of ecld
ecld.ogf_star_exp Star OGF of ecld
ecld.ogf_star_gamma_star Star OGF of ecld
ecld.ogf_star_hgeo Star OGF of ecld
ecld.op_O The O, V, U operators in option pricing model
ecld.op_Q The Q operator in option pricing model
ecld.op_Q_skew The Q operator in option pricing model
ecld.op_Q_skew_by_k_lm The Q operator in option pricing model
ecld.op_U_lag The O, V, U operators in option pricing model
ecld.op_V The O, V, U operators in option pricing model
ecld.op_VL_quartic The O, V, U operators in option pricing model
ecld.pdf Calculate the PDF of an ecld object
ecld.quartic Constructor of ecld class
ecld.quartic_model_sample Calculate ATM attributes from key quartic parameters
ecld.quartic_model_sample_attr Calculate ATM attributes from key quartic parameters
ecld.quartic_Q The ATM volatility and skew of Q_p in quartic model
ecld.quartic_Qp The ATM volatility and skew of Q_p in quartic model
ecld.quartic_Qp_atm_attr Calculate ATM attributes from key quartic parameters
ecld.quartic_Qp_atm_ki The ATM volatility and skew of Q_p in quartic model
ecld.quartic_Qp_atm_skew The ATM volatility and skew of Q_p in quartic model
ecld.quartic_Qp_rho The ATM volatility and skew of Q_p in quartic model
ecld.quartic_Qp_skew The ATM volatility and skew of Q_p in quartic model
ecld.quartic_SN0_atm_ki The ATM RNO related constants and calculations in quartic model
ecld.quartic_SN0_max_RNV The ATM RNO related constants and calculations in quartic model
ecld.quartic_SN0_rho_stdev The ATM RNO related constants and calculations in quartic model
ecld.quartic_SN0_skew The ATM RNO related constants and calculations in quartic model
ecld.sapply Wrappers for ecld to maintain consistent type between mpfr and numeric
ecld.sd Compute statistics analytically for an ecld object
ecld.sged_cdf The integral solutions of SGED
ecld.sged_const The integral solutions of SGED
ecld.sged_imgf The integral solutions of SGED
ecld.sged_mgf The integral solutions of SGED
ecld.sged_moment The integral solutions of SGED
ecld.sged_ogf The integral solutions of SGED
ecld.skewness Compute statistics analytically for an ecld object
ecld.solve Analytic solution for y(x) in lambda distribution
ecld.solve_by_poly Analytic solution for y(x) in lambda distribution
ecld.solve_isomorphic Analytic solution for y(x) in lambda distribution
ecld.solve_quartic Analytic solution for y(x) in lambda distribution
ecld.validate Constructor of ecld class
ecld.var Compute statistics analytically for an ecld object
ecld.y_slope Analytic solution for the slope of y(x) in lambda distribution
ecld.y_slope_trunc Analytic solution for the slope of y(x) in lambda distribution
ecldOrEcd-class The ecldOrEcd class
ecop-class An S4 class to represent the top-level option model
ecop.bs_call_price Calculate option price from implied volatility in Black-Sholes model
ecop.bs_implied_volatility Implied volatility of Black-Sholes model
ecop.bs_option_price Calculate option price from implied volatility in Black-Sholes model
ecop.bs_put_price Calculate option price from implied volatility in Black-Sholes model
ecop.build_opt Constructor of ecop class by read conf for option sample data
ecop.enrich_option_df Read option data csv
ecop.find_fixed_point_lambda_by_atm_skew Utility to find the fixed point lambda that matches ATM skew
ecop.find_fixed_point_sd_by_lambda Utility to find the fixed point stdev when lambda is given
ecop.from_symbol_conf Constructor of ecop class by read conf for option sample data
ecop.get_ld_triple Get triple list of ecld objects by stdev
ecop.opt-class An S4 class to represent the option data and model calculation
ecop.polyfit_option Poly fit on option prices
ecop.read_csv_by_symbol Read option data csv
ecop.read_symbol_conf Constructor of ecop class by read conf for option sample data
ecop.smile_data_calculator Master calculator for all the analytics of volatility smiles required for a date
ecop.term_atm Master calculator for all the analytics of volatility smiles required for a date
ecop.term_idx_range Produce 3x3 plot of volatility smiles for a date
ecop.term_master_calculator Master calculator for all the analytics of volatility smiles required for a date
ecop.term_plot_3x3 Produce 3x3 plot of volatility smiles for a date
ecop.term_realized_days Produce 3x3 plot of volatility smiles for a date
ecop.term_target_days_default Produce 3x3 plot of volatility smiles for a date
ecop.vix_plot_3x3 Produce 3x3 plot of VIX volatility smiles for a date
ellipticity Ellipticity of ecd object
ellipticity-method Ellipticity of ecd object
ellipticity.ecd Ellipticity of ecd object

-- H --

history List of history in the Elliptic DB
history-method List of history in the Elliptic DB
history.ecdb List of history in the Elliptic DB

-- I --

integrate_pdf Integrate a function with PDF of the distribution
integrate_pdf-method Integrate a function with PDF of the distribution
integrate_pdf.ecd Integrate a function with PDF of the distribution

-- J --

jinv J-invariant of the elliptic curve y(x)
jinv-method J-invariant of the elliptic curve y(x)
jinv.ecd J-invariant of the elliptic curve y(x)

-- K --

k2mnt Conversion between cumulants and moments
kqsl Stable lambda distribution
ksl Stable lambda distribution
kstablecnt Stable Count distribution
kstdlap Standardized Laplace process and distribution

-- L --

lamp Constructor of lamp class
lamp-class An S4 class to represent the lambda process
lamp.generate_tau Generate tau from stable distribution
lamp.plot_sim4 Plot the simulation result in standard layout
lamp.plot_sim6 Plot the simulation result in standard layout
lamp.qsl_fit_config Read QSLD fit config
lamp.qsl_fit_config_xtable Read QSLD fit config
lamp.qsl_fit_plot Plot the fit to asset returns using quartic stable lambda distribution
lamp.sd_factor Calculate sd adjustment factor
lamp.simulate1 Simulate one sequence of lambda process from stable distribution
lamp.simulate_iter Simulate lambda process from stable distribution iteratively
lamp.stable_rnd_walk Calculate the stable random walk
levy.dlambda Standard Lambda distribution
levy.domain_coloring Domain coloring of Laplace kernel of lambda distribution
levy.dskewed Skewed Levy distribution in Levy statistics

-- M --

mnt2k Conversion between cumulants and moments
moment Compute the moment of ecd via integration
moment-method Compute the moment of ecd via integration
moment.ecd Compute the moment of ecd via integration

-- N --

numericMpfr-class The numericMpfr class

-- P --

pec The Elliptic Distribution
plot_2x2 Standard 2x2 plot for sample data
plot_2x2-method Standard 2x2 plot for sample data
plot_2x2.ecd Standard 2x2 plot for sample data
pqsl Stable lambda distribution
psl Stable lambda distribution
pstablecnt Stable Count distribution
pstdlap Standardized Laplace process and distribution

-- Q --

qec The Elliptic Distribution
qqsl Stable lambda distribution
qsl Stable lambda distribution
qsld Constructor of sld class
qsld.fit Fit observations to QSLD via MLE
qsl_kurtosis_analytic Analytic solutions on the statistics of quartic stable lambda distribution
qsl_pdf_integrand_analytic Analytic solutions on the statistics of quartic stable lambda distribution
qsl_skewness_analytic Analytic solutions on the statistics of quartic stable lambda distribution
qsl_std_pdf0_analytic Analytic solutions on the statistics of quartic stable lambda distribution
qsl_variance_analytic Analytic solutions on the statistics of quartic stable lambda distribution
qstablecnt Stable Count distribution
qstdlap Standardized Laplace process and distribution
quantilize Add the quantile data to the ecd object
quantilize-method Add the quantile data to the ecd object
quantilize.ecd Add the quantile data to the ecd object

-- R --

read Read API for the ecdb
read-method Read API for the ecdb
read.ecdb Read API for the ecdb
rec The Elliptic Distribution
rlaplace0 Laplace distribution
rqsl Stable lambda distribution
rsl Stable lambda distribution
rstablecnt Stable Count distribution
rstdlap Standardized Laplace process and distribution

-- S --

sld Constructor of sld class
sld-class An S4 class to represent the stable lambda distribution
sld.kurt Compute statistics analytically for an sld object
sld.kurtosis Compute statistics analytically for an sld object
sld.mean Compute statistics analytically for an sld object
sld.sd Compute statistics analytically for an sld object
sld.skewness Compute statistics analytically for an sld object
sld.var Compute statistics analytically for an sld object
solve-method Solve the elliptic curve y(x)
solve.ecd Solve the elliptic curve y(x)
solve_sym Analytic solution for a symmetric elliptic curve
solve_sym-method Analytic solution for a symmetric elliptic curve
solve_sym.ecd Analytic solution for a symmetric elliptic curve
solve_trig Trigonometric solution for a elliptic curve
solve_trig-method Trigonometric solution for a elliptic curve
solve_trig.ecd Trigonometric solution for a elliptic curve
summary Summary for the Elliptic DB (ECDB)
summary-method Summary for the Elliptic DB (ECDB)
summary.ecdb Summary for the Elliptic DB (ECDB)

-- W --

write Write API for the ecdb for a list of basic ecdattr objects
write-method Write API for the ecdb for a list of basic ecdattr objects
write.ecdb Write API for the ecdb for a list of basic ecdattr objects

-- Y --

y_slope Slope of y(x)
y_slope-method Slope of y(x)
y_slope.ecd Slope of y(x)