The Combinational Mutation Strategy of Differential Evolution Algorithm for Pricing Vanilla Options and Its Implementation on Data during Covid-19 Pandemic

Paper: arXiv 2301.09261

Authors: Werry Febrianti, Kuntjoro Adji Sidarto, Novriana Sumarti

Abstract

Investors always want to know about the profit and the risk that they will be get before buying some assets. Our main focus is getting the profit and the probability of getting that profit using the differential evolution algorithm for vanilla option pricing on data before and during COVID-19 pandemic. Therefore, we model the pricing of an option using a bi-objective optimization problem using data before and during COVID-19 pandemic for one year expiration date. We change this problem into an optimization problem using adaptive weighted sum method. We use metaheuristics algorithm like Differential Evolution (DE) algorithm to solve this bi-objective optimization problems. In this paper, we also use modification of Differential Evolution for getting Pareto optimal solutions on vanilla option pricing for all contract. The algorithm is called Combinational Mutation Strategy of Differential Evolution (CmDE) algorithm. The results of our algorithm are satisfactory close to the real option price in the market data. Besides that, we also compare our result with the Black-Scholes results for validation. The results show that our results can approximate the real market options more accurate than Black-Scholes results. Hence, our bi-objective optimization using Combinational Mutation Strategy of Differential Evolution algorithm can be used to approximate the market real vanilla option pricing before and during COVID-19 pandemic.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 5.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel application of a modified Differential Evolution algorithm (CmDE) to a bi-objective optimization model for vanilla option pricing during market turbulence. While it successfully outperforms the standard Black-Scholes baseline empirically, the overall methodology relies heavily on heuristic optimization rather than deep stochastic calculus, and the empirical testing is somewhat limited in scope.

Research Flowchart

  flowchart TD
    A[Research Goal: Accurate Vanilla Option Pricing Before & During COVID-19] --> B[Data Inputs: Historical Market Data & 1-Year Option Expiration]
    B --> C[Model Formulation: Bi-Objective Optimization Problem]
    C --> D[Problem Transformation: Adaptive Weighted Sum Method]
    D --> E[Optimization: Combinational Mutation Strategy of Differential Evolution - CmDE]
    E --> F[Validation: Performance Comparison against Black-Scholes Model]
    F --> G[Outcome: CmDE Outperforms Black-Scholes in Approximating Real Market Prices]