python - obtain weird result when solving the integration problem

Question

The problem is to solve gamma first, and then plug gamma into the second equation to get k*, but I could not figure out why my K* is always 1.0. Any help would be appreciated, and if this problem could be solved in python, that would be great also.

Here is my attempt,

T = 1;
sigma = 0.3;
r = 0.09;
a = r - sigma^2/2;
K = 100;
S_0 = 100;
M = 3;

syms gamma Kstar t; 
eqa = int(S_0*exp(exp(3*t*(T-t/2)*gamma*sigma/T^2 + a*t + sigma^2*(t- 3*t^2*(T - t/2)^2/T^3)/2)), t, 0, T) == T*K;
Y = vpasolve(eqa,gamma);
K_s = solve((log(log(Kstar)) - log(M))*T/sigma == Y, Kstar);
display(K_s);

And here is my attempt by python

import scipy.integrate as integrate
import scipy.special as special
from scipy.integrate import quad
from numpy import exp, log
from sympy.solvers import solve
from sympy import Symbol
T = 1
sigma = 0.3
r = 0.09
a = r - sigma**2/2
K = 100
S_0 = 100
M_2 = S_0 * exp(r*T/2 - sigma**2*T/12)

t = Symbol("t")
Kstar = Symbol("Kstar")
gamma = Symbol("gamma")

def integrand(t, gamma):
    return S_0*exp(exp(3*t*(T-t/2)*gamma*sigma/T**2 + a*t + sigma**2*(t- 3*t**2*(T - t/2)**2/T**3)/2))

eqa = quad(integrand, 0, T, args(gamma)) == K*T

result = solve(eqa, gamma)
print(result)

And this bug occured

NameError                                 Traceback (most recent call last)
<ipython-input-10-e24a1238ff27> in <module>
     20     return S_0*exp(exp(3*t*(T-t/2)*gamma*sigma/T**2 + a*t + sigma**2*(t- 3*t**2*(T - t/2)**2/T**3)/2))
     21 
---> 22 eqa = quad(integrand, 0, T, args(gamma)) == K*T
     23 
     24 result = solve(eqa, gamma)

NameError: name 'args' is not defined

Thanks a lot

question from:https://stackoverflow.com/questions/65867091/obtain-weird-result-when-solving-the-integration-problem

Answer 1

why did you call args here, thats not a function args(gamma) please explain what you want it to do