2014/10/06 by Jarno Talponen, Talponen, Jarno
Economics, Econometrics and Finance · Mathematics · #91G10 #91G20 #Economic theories and models #FOS: Economics and business #FOS: Mathematics #General Finance (q-fin.GN) #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Trading and Market Microstructure (q-fin.TR) #math.PR #msc:91G10 #msc:91G20 #q-fin.GN #q-fin.MF #q-fin.PR #q-fin.TR
paper · pdf · doi:10.48550/arxiv.1410.1426
arxiv created 2014/10/06 · openalex publication_date 2014/10/06 · arxiv updated 2014/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A motivating question in this paper is whether a sensible investment strategy may systematically contain long positions in out-of-the-money European calls with short expiry. Here we consider a very simple trading strategy for calls. The main points of this note are the following. First, the presented trading strategy appears very lucrative in the Black-Scholes-Merton (BSM) framework. In fact, it is such even to the extent that the BSM model turns out to be, in a sense, incompatible with the CAPM. Second, if one wishes to adapt these models together, then the adjustment of the consistent pricing rule (i.e. modifying state price densities) inevitably leads to some form of volatility smile and this is the main point of the paper. Moreover, these observations arise from purely structural considerations.