Memperkirakan Spread Bid-Ask

Di bawah ini saya berikan vektornya Oktaf fungsi untuk memperkirakan spread bid-ask dari harga tertinggi, terendah dan penutupan sesuai dengan “Cara Sederhana untuk Memperkirakan Spread Bid-Ask dari Harga Tertinggi dan Terendah Harian,” (Corwin dan Schultz, 2012). Makalah ini dapat diunduh dari salah satu beranda penulis di https://www3.nd.edu/~scorwin/, di mana seseorang juga dapat menemukan lembar kerja yang menunjukkan perhitungan yang terlibat.

## Copyright (C) 2018 dekalog
## 
## This program is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## 
## You should have received a copy of the GNU General Public License
## along with this program.  If not, see .

## -*- texinfo -*- 
## @deftypefn {} {@var{spread}, @var{spread_0 =} bid_ask_spread (@var{high}, @var{low}, @var{close})
##
## This function takes vectors of observed high, low and close prices and calculates
## the closed form bid-ask spread, as outlined in 
##
## "A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices"
## ( Corwin and Schultz, 2012 )
##
## The first output is the bid-ask spread with zero values interpolated by use
## of an Exponential moving average (default value of 20 bars) whilst the 
## second output is the bid-ask spread without this interpolation, and hence
## possibly contains zero values.
##
## Paper available at https://www3.nd.edu/~scorwin/
##
## @seealso{}
## @end deftypefn

## Author: dekalog 
## Created: 2018-12-11

function [ spread2 , spread ] = bid_ask_spread ( high , low , close )
  
  hilo_ratio_1 = high ./ low ;
  hilo_ratio_2 = max( [ high shift( high , 1 ) ] , [] , 2 ) ./ min( [ low shift( low , 1 ) ] , [] , 2 ) ;
  
  % adjust for overnight price gaps
  % gap up
  close_shift = shift( close , 1 ) ; close_shift( 1 ) = low( 1 ) ;
  ix = find( low > close_shift ) ;
  if ( ~isempty( ix ) )
    estimated_overnight_price_increases = low( ix ) .- close( ix .- 1 ) ;
    hilo_ratio_1( ix ) = ( high( ix ) .- estimated_overnight_price_increases ) ./ ( low( ix ) .- estimated_overnight_price_increases ) ;
    hilo_ratio_2( ix ) = max( [ ( high( ix ) .- estimated_overnight_price_increases ) high( ix .- 1) ] , [] , 2 ) ...
                         ./ min( [ ( low( ix ) .- estimated_overnight_price_increases ) low( ix .- 1 ) ] , [] , 2 ) ;
  endif
  
  % gap down
  close_shift( 1 ) = high( 1 ) ;
  clear ix ;
  ix = find( high < close_shift ) ;
  if ( ~isempty( ix ) )
    estimated_overnight_price_decreases = close( ix .- 1 ) .- high( ix ) ;
    hilo_ratio_1( ix ) = ( high( ix ) .+ estimated_overnight_price_decreases ) ./ ( low( ix ) .+ estimated_overnight_price_decreases ) ;
    hilo_ratio_2( ix ) = max( [ ( high( ix ) .+ estimated_overnight_price_decreases ) high( ix .- 1) ] , [] , 2 ) ...
                         ./ min( [ ( low( ix ) .+ estimated_overnight_price_decreases ) low( ix .- 1 ) ] , [] , 2 ) ;
  endif
  
  beta = log( hilo_ratio_1 ) .^ 2 ; beta = beta .+ shift( beta , 1 ) ;
  gamma = log( hilo_ratio_2 ) .^ 2 ;
  alpha = ( sqrt( 2 .* beta ) .- sqrt( beta ) ) ./ ( 3 .- 2 .* sqrt( 2 ) ) .- sqrt( gamma ./ ( 3 .- 2 .* sqrt( 2 ) ) ) ;
  
  spread = exp( alpha ) ; spread = 2 .* ( spread .- 1 ) ./ ( 1 .+ spread ) ;
  spread( 1 ) = spread( 2 ) ; spread( spread < 0 ) = 0 ;
  
  ndays = 20 ;
  ema_alpha = 2 / ( ndays + 1 ) ;
  avg = filter( ema_alpha , [ 1 ema_alpha - 1 ] , spread , spread(1) ) ;

  clear ix ;
  spread2 = spread ;
  ix = find( spread == 0 ) ; spread2( ix ) = avg( ix ) ;
  
endfunction

Dengan menggunakan data pada spreadsheet tersebut, kedua keluaran fungsi akan terlihat seperti ini:

garis hitam adalah spread yang diinterpolasi menggunakan rata-rata bergerak eksponensial di mana perhitungan spread mentah adalah nol (ini adalah tambahan saya sendiri) dan garis merah adalah spread tanpa interpolasi. Catatan: sumbu y dinyatakan sebagai nilai persentase.

Alasan mengapa seseorang mungkin menggunakan fungsi ini diuraikan dalam makalah yang ditautkan di atas. Selamat menikmati!