2014/11/06 by Francesco Caravenna, Caravenna, Francesco, Jacopo Corbetta +1
Economics, Econometrics and Finance · Mathematics · #60G44 #91B25 #91G20 #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #math.PR #msc:60G44 #msc:91B25 #msc:91G20 #q-fin.PR
paper · pdf · doi:10.48550/arxiv.1411.1624
35 pages, 2 figures. To appear on SIAM Journal on Financial Mathematics
arxiv created 2016/07/07 · arxiv updated 2016/07/08
We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with arbitrary strike) and extreme strike (with arbitrary bounded maturity), extending previous work of Benaim and Friz [Math. Finance 19 (2009), 1-12]. We present applications to popular models, including Carr-Wu finite moment logstable model, Merton's jump diffusion model and Heston's model.