Short-time expansions for close-to-the-money options under a L 'evy jump\n model with stochastic volatility

2014/04/02 by José E. Figueroa‐López, Figueroa-López, José E., Sveinn Ólafsson +2 · 1 citation
Business, Management and Accounting · Economics, Econometrics and Finance · Mathematics · #60F99 #60G51 #91G20 #91G60 #Advanced Queuing Theory Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1404.0601

openalex publication_date 2014/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In Figueroa-L 'opez et al. (2013), a second order approximation for\nat-the-money (ATM) option prices is derived for a large class of exponential\nL 'evy models, with or without a Brownian component. The purpose of this\narticle is twofold. First, we relax the regularity conditions imposed in\nFigueroa-L 'opez et al. (2013) on the L 'evy density to the weakest possible\nconditions for such an expansion to be well defined. Second, we show that the\nformulas extend both to the case of "close-to-the-money" strikes and to the\ncase where the continuous Brownian component is replaced by an independent\nstochastic volatility process with leverage.\n

Citations

• Foundations of Modern Probability

Cited by

• Correction to Black-Scholes formula due to fractional stochastic\n volatility

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