Issues with greek effects profit and loss calculations, for a short strangle, not matching actual profit

S2 = 88; %Stock price at time of trade, 00:15am on 04/18/2025 (Friday) AUS time, or 10:08am US time 04/17/25 (Thursday)
K = 93;
c2 = 3.75; 
p2 = 8.75;  
T2 = days252bus("04/18/2025","05/09/2025")/252;
rf = 0.043447; 
y = 0;

IV_of_Call_Exit_Trade = bsm_ivol(S2, K, rf, y, T2, 'c', c2, x0)
IV_of_Call_Exit_Trade = 0.6868
IV_of_Put_Exit_Trade= bsm_ivol(S2, K, rf, y, T2, 'p', p2, x0)
IV_of_Put_Exit_Trade = 0.7146
Total gain/loss
%Portfolio opening value 
port_1 = (c1+p1)*qty 
port_1 = -1400
%Portfolio closing value 
port_2 = (c2+p2)*qty 
port_2 = -1250
%gain/loss 
profit = port_2-port_1
profit = 150
%My short straddle strategy made a proft of $150
Greek effects
%Change in underlying variables 
Change_in_AMD_Stock_Price = S2-S1;
Change_in_time = days252bus("04/18/2025","05/09/2025")/252 - days252bus("04/15/2025","05/09/2025")/252
Change_in_time = -0.0119
% Delta effect
Delta_Effect = delta1*Change_in_AMD_Stock_Price
Delta_Effect = 137.7018
% Gamma effect
Gamma_Effect = (1/2)*gamma1*(Change_in_AMD_Stock_Price^2)
Gamma_Effect = -116.6401
% Theta effect
Theta_Effect = Change_in_time*theta1
Theta_Effect = -0.4792
% Vega effect
Vega_Effect = (IV_of_Call_Exit_Trade-IV_of_Call_Actual_Trade)*vega1_c*qty+(IV_of_Put_Exit_Trade-IV_of_Put_Actual_Trade)*vega1_p*qty
Vega_Effect = 21.7712
% Total greek effect
Total_Explained_Effect_by_Greeks = Delta_Effect+Gamma_Effect+Theta_Effect+Vega_Effect
Total_Explained_Effect_by_Greeks = 42.3537
Unexplaied P&L 
Unexplained_Effects = profit - Total_Explained_Effect_by_Greeks
Unexplained_Effects = 107.6463

[Alex]

The main issue is that the out of the total profit made of $150, the "Total Explained Effect by Greeks = 42.3537" with the remaining "Unexplained Effects = 107.6463". In reality the greek effects should have explained the vast majority of the $150 profit, my question is, did I make an error on my code that could explain why the total profit explained by the greeks is so small?

Answer 1

[Shlok]

Hi Alex,

Based on the provided code, I’ve assumed a few things since some variables seem to be missing. It looks like you're using exit-day Greeks to explain P&L changes that occurred between entry and exit. However, Greeks are sensitivities, and they’re only meaningful when applied at the start of a move or averaged over the holding period to reflect actual changes in price and implied volatility. To improve accuracy, consider using average Greeks over the period. Also, ensure all Greeks are expressed in dollar terms using appropriate contract multipliers, and double-check that your units are consistent.

You can also refer to the following resources for further understanding:

• https://www.britannica.com/money/option-greeks-delta-theta-gamma-vega
• https://quant-next.com/option-greeks-and-pl-decomposition-part-1/