This paper studies implied volatility smirk quantitatively. We first propose a new concept of smirkness, which is defined as a triplet of at-the-money implied volatility, skewness (slope at the money) and smileness (curvature at the money) of implied volatility – moneyness curve. The moneyness is the logarithm of the strike price over the forward price, normalized by the standard deviation of e...

The illiquidity of long-maturity options has made it difficult to study the term structures of option spanning portfolios. This paper proposes a new estimation and inference framework for these option-implied term structures that addresses long-maturity illiquidity. By building a sieve estimator around the risk-neutral valuation equation, the framework theoretically justifies (fattailed) extrap...

Abstract In this paper, we characterize two deterministic implied volatility models, defined by assuming that either the per-delta or the per-strike implied volatility surface has a deterministic evolution. Practitioners have recently proposed these two models to describe two regimes of implied volatility (see Derman (1999 Risk 4 55–9)). In an arbitrage-free sticky-delta model, we show that the...

The phenomenon of isoscaling is receiving considerable interest because of its relation with the symmetry term in statistical [1] and dynamical [2] descriptions of fragmentation reactions. As reported recently, the symmetry term coefficient γ in the liquid-drop description of the nascent fragments appears to be decreasing from the standard value γ = 25 MeV for isolated nuclei to about 15 MeV or...

The essay examines the intersection between aesthetic the-ory and representations of city in periodical Spectator (1711-1714). Focusing on this allows for an analysis cultural work pleasure is supposed to do according Spectator, also shows key differenc-es “spectatorial” later, Kantian aesthetics. In has with producing a model how one should relate realm politics—rather than disin-terest, preco...

Abstract We argue that double inflation may occur when a spectator field is non-minimally coupled to gravity. As concrete example, we study two-field inflationary model where the initial gravity while inflaton minimally coupled. The non-minimal coupling results in growth of which, turn, drives second stage significant region parameter space. isocurvature fluctuations originating from source adi...

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