arXiv subjects

Michele Domenico Massaria

Publications and source records attributed to Michele Domenico Massaria.

3 recordsLinked to original sources

arXiv2026

Smile asymptotics for Bachelier implied volatility

We investigate the asymptotic behaviour of the Bachelier implied volatility tails, extending the large-strike results established for the Black-Scholes implied volatility. Exploiting the theory of regular variation, we derive explicit expressions for the Bachelier implied volatility in the wings of the smile, directly linking them to the tail decay of the underlying returns' distribution. Furthermore, we establish a rigorous connection between the analyticity strip of the characteristic function and the asymptotic slope of the volatility smile. Moreover, we show that if the implied variance grows linearly for large absolute moneyness degree, the underlying returns' distribution must exhibit exponential tail decay, and the corresponding characteristic function is analytic in a horizontal strip of the complex plane. These findings characterise valid models based solely on the observable asymptotic behaviour of the smile.

q-fin.PR↗

arXiv2026

Modeling dependence in sparse time series of Insurance Claims

Modeling the dependence between multiple risk types is a central challenge in contemporary insurance risk management. The standard approaches, Lévy copulas and zero-mixed models, often face practical difficulties in simulation and parameter calibration. In this paper, we introduce the Comb-Bernoulli model, a novel framework for capturing dependence between sparse time series of insurance risks, bridging the benefits of the two standard approaches. The (traditional) copula structure of the proposed model enables tractable: i) simulation, ii) likelihood evaluation, and iii) estimation of dependence parameters. We present the general properties of the model and analyze in detail the Gaussian copula case with lognormal marginals. Moreover, we illustrate an application using the Danish fire insurance dataset, highlighting both the modeling strengths and numerical efficiency of our approach in real-world risk management.

q-fin.RM↗

arXiv2026

The additive Bachelier model with an application to the oil option market in the Covid period

In April 2020, the Chicago Mercantile Exchange temporarily switched the pricing formula for West Texas Intermediate oil market options from the Black model to the Bachelier model. In this context, we introduce an additive Bachelier model that provides a simple closed-form solution and a good description of the implied volatility surface. This new additive model exhibits several notable mathematical and financial properties. It ensures the no-arbitrage condition, a critical requirement in highly volatile markets, while also enabling a parsimonious synthesis of the volatility surface. The model features only three parameters, each with a clear financial interpretation: the volatility term structure, the vol-of-vol, and a parameter for modelling skew. Model calibration can follow a cascade procedure: first, it accurately replicates the term structures of forwards and At-The-Money volatilities observed in the market; second, it fits the smile of the volatility surface. The proposed model also supports efficient pricing of path-dependent exotic options via Monte Carlo simulation, using a straightforward and computationally efficient approach. Overall, this model provides a robust and parsimonious description of the oil option market during the exceptionally volatile first period of the Covid-19 pandemic.

q-fin.MF↗