2018/03/27 by Axel A. Araneda, Araneda, Axel A., Marcelo Villena +2
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Black–Scholes model #Capital Investment and Risk Analysis #Computational Finance (q-fin.CP) #Constant elasticity of variance model #Econometrics #Elasticity (physics) #FOS: Economics and business #Implied volatility #Leverage (statistics) #Local volatility #Mathematical economics #Mathematics #Physics #SABR volatility model #Semiclassical physics #Statistics #Stochastic processes and financial applications #Stochastic volatility #Valuation of options #Volatility (finance) #Volatility smile #q-fin.CP
paper · pdf · doi:10.48550/arxiv.1803.10376
openalex publication_date 2018/03/27 · arxiv created 2018/03/28 · arxiv updated 2018/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The Constant Elasticity of Variance (CEV) model significantly outperforms the\nBlack-Scholes (BS) model in forecasting both prices and options. Furthermore,\nthe CEV model has a marked advantage in capturing basic empirical regularities\nsuch as: heteroscedasticity, the leverage effect, and the volatility smile. In\nfact, the performance of the CEV model is comparable to most stochastic\nvolatility models, but it is considerable easier to implement and calibrate.\nNevertheless, the standard CEV model solution, using the non-central chi-square\napproach, still presents high computational times, specially when: i) the\nmaturity is small, ii) the volatility is low, or iii) the elasticity of the\nvariance tends to zero. In this paper, a new numerical method for computing the\nCEV model is developed. This new approach is based on the semiclassical\napproximation of Feynman's path integral. Our simulations show that the method\nis efficient and accurate compared to the standard CEV solution considering the\npricing of European call options.\n