Optimal Prediction of Resistance and Support Levels under Constant Elasticity of Variance Processes

Battle Count: 82

The paper directly addresses the prediction of resistance and support levels, which are fundamental concepts in technical analysis and algorithmic trading. The CEV model captures the empirically observed leverage effect (inverse price-volatility relationship), making it more realistic than GBM for equity markets. However, the paper is primarily theoretical, the upper boundary interpretation is non-standard (model-invalidation rather than selling level), and no empirical validation is provided. The admissibility conditions on the aspiration level distribution may limit practical applicability. The strict local martingale property introduces mathematical subtleties that may not translate directly into trading signals.

Implementation requires: (1) computing the CEV transition density involving modified Bessel functions of the first kind, (2) solving coupled nonlinear integral equations via backward-induction discretization, (3) handling the strict local martingale property and its implications for the stopping region, (4) verifying admissibility conditions on the aspiration level distribution, and (5) managing the boundary behavior where c(T-) = infinity. The mathematical framework is sophisticated, requiring expertise in stochastic calculus, free-boundary problems, and numerical analysis of integral equations.

The paper provides complete mathematical proofs, explicit parameter settings for numerical examples (mu, sigma, beta, lambda, T), and describes the backward-induction discretization method for solving the integral equations. However, no code repository or detailed algorithm pseudocode is provided. The numerical results are illustrative rather than a standalone numerical method. Reproduction would require implementing the CEV transition density (involving modified Bessel functions) and the coupled nonlinear integral equations.