A new efficient numerical method for solving American option under regime switching model

A new efficient numerical method for solving American option under regime switching model

1. Introduction

   • Problem: Valuation of American options under regime change models.
   • Solution: Efficient numerical method using frontal fixation transformation and explicit finite differences.

2. Regime Change Model:

   • Uses a continuous-time Markov chain.
   • Variable parameters such as volatility and risk-free interest rate.

3. Border Problem Free:

   • Description of the coupled free boundary problem for American put options.
   • Frontal fixation transformation to simplify the domain.

4. Numerical Method:

   • Application of explicit finite differences.
   • Numerical scheme conditionally stable and consistent.
   • Calculation of option prices and optimal exercise boundaries.

5. Numerical Analysis:

   • Stability and consistency of the method.
   • Comparison with other known methods (penalty methods and binomial trees).

6. Conclusions:

   • El método propuesto es eficiente y preciso para la valoración de opciones americanas bajo modelos de cambio de régimen.
   • It allows the calculation of option prices and optimal exercise boundaries in an effective manner.

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