Convexity of price curve - curve fitting or non-linear regression

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Convexity of price curve - curve fitting or non-linear regression

posted

Getting Started Momentum Statistics

Hi All,

This is a newbie question, please be indulgent.

I'm looking to fit the price of a security to a simple quadratic in time model:

Pt=alpha+beta*t+gamma*t^2

what i'm looking for is the gamma value. This will enable me to know if the price is convex or not. I want to test if the behavior of prices is somewhat different depending on this indicator.

However, i quite sadly failed to implement this logic in my Notebook coding

from scipy.optimize import curve_fit  
import statsmodels.formula.api as sm

PGJ = get_pricing(  
    assets,  
    fields='close_price', #modify to price, open_price, high, low or volume to change the field  
    start_date='2015-01-01', #customize your pricing date range  
    end_date = '2016-06-01',  
    frequency='daily', #change to daily for daily pricing  
)

# statsmodels.formula.api fails  
data = {"C":PGJ.values, "t":PGJ.index.values}  
model = sm.ols(formula = 'a ~ np.power(t, 2) + t ', data = data).fit()


#  scipy.optimize import fails  
def func(x, alpha,beta,gamma):  
  return gamma*np.power(x, 2) + beta*x+gamma

popt, pcov = curve_fit(func, PGJ.index.values, PGJ.values,p0=(1,1,1))

I'm pretty much at a dead end... Has anyone please tried and succeeded to get this data ?

Thank you for your kind assistance

3 responses

hi all,

Got a nice answer from Lotanna Ezenwa of quantopian. package scipy.optimize has been made available


def func1(x, gamma,beta,alpha):  
  return gamma*np.power(x, 2) + beta*x + alpha

#PGJ.values[:,0]

length_values=len(np.array(PGJ.values[:,0]))  
arr=np.array([0.0])  
for i in range(1,length_values):  
    arr=np.append(arr,(1.0/length_values)*i)

popt, pcov = curve_fit(func1, arr, np.array(PGJ.values[:,0]))

this ugly code results in the following result:

Curve= 20.08963115.t^2 + -27.69074113.t+ 39.13609521

Behavioral Trader

Why fit something driven by the whim and fund flow of the masses, into some elegant but useless curve?

Because of behvioral bias my friend. as you should have guessed :-)

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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian.

In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.