ThinkorSwim Imp_Vol Function

EM

I am having issues on matching the output on Ameritrade's ThinkorSwim Imp_Vol function. They use a reverse calculate based on the marks of the options, based off the Bjerksund-Stensland model.

This is what I have right now and I would appreciate any help on it.

def implied_volatility_put(underlying_price, exercise_price, time_in_years, risk_free_rate, option_price):
high = 5
low = 0

while (high - low) > 0.0001:
    if bjerksund_stensland_put(underlying_price, exercise_price, time_in_years, risk_free_rate, (high + low) / 2) > option_price:
        high = (high + low) / 2
    else:
        low = (high + low) / 2

return (high + low) / 2

def bjerksund_stensland_put(underlying_price, exercise_price, time_in_years, risk_free_rate, volatility):
div = 1E-08
z = -1
rr = div
dd = rr
dd2 = 2 * dd - rr
asset_new = underlying_price
underlying_price = exercise_price
exercise_price = asset_new

dt = volatility * sqrt(time_in_years)
drift = risk_free_rate - div
v2 = volatility**2

b1 = sqrt((z * drift / v2 - 0.5)**2 + 2 * rr / v2)
beta = (1 / 2 - z * drift / v2) + b1
binfinity = beta / (beta - 1) * exercise_price
bb = max(exercise_price, rr / dd2 * exercise_price)
ht = -(z * drift * time_in_years + 2 * dt) * bb / (binfinity - bb)
i = bb + (binfinity - bb) * (1 - exp(ht))
    
if underlying_price < i and beta < 100: # To avoid overflow
    alpha = (i - exercise_price) * i**(-beta)
    return alpha * underlying_price**beta - alpha * phi(underlying_price, time_in_years, beta, i, i, rr, z * drift, volatility) + phi(underlying_price, time_in_years, 1, i, i, rr, z * drift, volatility) - phi(underlying_price, time_in_years, 1, exercise_price, i, rr, z * drift, volatility) - exercise_price * phi(underlying_price, time_in_years, 0, i, i, rr, z * drift, volatility) + exercise_price * phi(underlying_price, time_in_years, 0, exercise_price, i, rr, z * drift, volatility)

return underlying_price - exercise_price

Parameters

underlying_price: Price of underlying asset

exercise_price: Exercise price of the option

time_in_years: Time to expiration in years (ie. 33 days to expiration is 33/365)

risk_free_rate: Risk free rate (ie. 2% is 0.02)

volatility: Volatility percentage (ie. 30% volatility is 0.30)

bigdavediode

Here's the code I previously posted to do exactly that:

https://community.backtrader.com/topic/785/calculate-an-option-s-implied-volatility-using-gbs-bjerksund-stensland-2002