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Asian Options Pricing


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This project focuses on the application and comparison of several option pricing models, specifically:

  • Binomial Model
  • Black-Scholes Model
  • Trinomial Model
  • Monte Carlo Simulation (with and without variance reduction)

The primary objective is to compare the prices obtained through these models and analyze their convergence under various scenarios. The results will be documented in a comprehensive written report.




Options Under Study


The project explores exotic options such as:

  1. Asian Options (Geometric and Arithmetic Average)
  2. Barrier Options (Knock-In and Knock-Out)
  3. Binary Options (Asset-or-Nothing and Cash-or-Nothing)

The underlying assets considered are non-dividend-paying stocks.





Key Tasks


  1. Risk-Free Rate (r) and Volatility (σ) Estimation
    • Retrieve risk-free rates from data providers like FactSet or Bloomberg.
    • Consider two scenarios: crisis and expansion, each with different rrr and σ\sigmaσ.
    • Estimate volatility using historical data, with separate values for positive and negative market periods.
  2. Black-Scholes Formula Development
    • Implement Python functions for pricing Barrier and Binary Options using closed-form solutions.
    • Focus on European-style calls for Barrier Options, including Up-and-In, Up-and-Out, Down-and-In, and Down-and-Out types.
  3. Monte Carlo Simulation for Barrier and Binary Options
    • Develop Python functions to generate sample paths using the Geometric Brownian Motion (GBM) process.
    • Include variance reduction techniques, such as antithetic variables.
  4. Binomial and Trinomial Models
    • Implement Binomial and Trinomial Tree Models in Python for Barrier and Binary Options.
  5. Asian Options Pricing
    • Use Monte Carlo methods for Geometric and Arithmetic Asian Options.
    • Implement the closed-form Black-Scholes solution for Arithmetic Asian Options.





Outcome


In conclusion, our study highlights the importance of variance reduction techniques in pricing Asian options, significantly lowering standard errors, especially for in-the-money options. Volatility estimation plays a crucial role, as discrepancies can impact pricing, particularly for out-of-the-money options. For barrier options, we combined lattice-based models with Monte Carlo simulations, using interpolation to improve accuracy. In pricing binary options, Monte Carlo with antithetic variates outperformed lattice models. Overall, volatility estimation remains key to accurate pricing. Despite the complexities of these options, understanding pricing techniques can provide valuable opportunities for risk management and profit optimization.



Miura Financial Research on LinkedIn