Martino Grasselli

@article{grasselli_2744,

title = {A general framework for a joint calibration of VIX and VXX options},

author = {Martino Grasselli and Andrea Mazzoran and Andrea Pallavicini},

url = {https://ideas.repec.org/a/spr/annopr/v336y2024i1d10.1007_s10479-023-05205-9.html},

year  = {2024},

date = {2024-05-01},

journal = {Annals Of Operations Research},

volume = {336},

number = {1},

pages = {3-26},

abstract = {We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure. Inspired by recent developments in commodity smile modelling, we present a multi-factor stochastic-local volatility model that is able to jointly calibrate plain-vanilla options both on VIX futures and VXX notes, thus going beyond the failure of purely stochastic or simply local-volatility models. We discuss numerical results on real market data by highlighting the impact of model parameters on implied volatilities.},

note = {https://arxiv.org/abs/2012.08353},

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@article{grasselli_2053,

title = {A fully quantization-based scheme for FBSDEs},

author = {Martino Grasselli and Gorgia Callegaro and Alexandro Gnoatto},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0096300322007251},

year  = {2023},

date = {2023-03-01},

journal = {Applied Mathematics And Computation},

volume = {441},

pages = {127666},

abstract = {We propose a quantization-based numerical scheme for a family of decoupled forward-backward stochastic differential equations. We simplify the scheme for the control in Pages and Sagna(2018) so that our approach is fully based on recursive marginal quantization and does not involveany Monte Carlo simulation for the computation of conditional expectations. We analyse in detail thenumerical error of our scheme and provide some examples of application to financial mathematics.},

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@article{garcin_2065,

title = {Long versus short time scales: the rough dilemma and beyond},

author = {Matthieu Garcin and Martino Grasselli},

url = {https://link.springer.com/article/10.1007/s10203-021-00358-3},

year  = {2022},

date = {2022-06-01},

journal = {Decisions in Economics and Finance},

volume = {45},

pages = {257-278},

abstract = {Using a large dataset on major FX rates, we test the robustness of the rough fractional volatility model over different time scales, by including smoothing and measurement errors into the analysis. Our findings lead to new stylized facts in the log-log plots of the second moments of realized variance increments against lag which exhibit some convexity in addition to the roughness and stationarity of the volatility. The very low perceived Hurst exponents at small scales are consistent with the rough framework, while the higher perceived Hurst exponents for larger scales lead to a nonlinear behaviour of the log-log plot that has not been described by models introduced so far.},

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@article{callegaro_1138,

title = {Fast Hybrid Schemes for Fractional Riccati Equations (Rough is not so Tough)},

author = {Gorgia Callegaro and Martino Grasselli and Gilles Pagès},

url = {https://pubsonline.informs.org/doi/10.1287/moor.2020.1054},

year  = {2021},

date = {2021-02-01},

journal = {Mathematics Of Operations Research},

volume = {46},

number = {1},

pages = {221-254},

abstract = {We solve a family of fractional Riccati equations with constant (possibly complex) coefficients. These equations arise, for example, in fractional Heston stochastic volatility models, which have received great attention in the recent financial literature because of their ability to reproduce a rough volatility behavior. We first consider the case of a zero initial value corresponding to the characteristic function of the log-price. Then we investigate the case of a general starting value associated to a transform also involving the volatility process. The solution to the fractional Riccati equation takes the form of power series, whose convergence domain is typically finite. This naturally suggests a hybrid numerical algorithm to explicitly obtain the solution also beyond the convergence domain of the power series. Numerical tests show that the hybrid algorithm is extremely fast and stable. When applied to option pricing, our method largely outperforms the only available alternative, based on the Adams method.},

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@article{grasselli_1264,

title = {VIX vs VXX: A Joint Analytical Framework},

author = {Martino Grasselli and Lakshithe Wagalath},

url = {https://www.worldscientific.com/doi/abs/10.1142/S0219024920500338},

year  = {2020},

date = {2020-09-01},

journal = {International Journal of Theoretical and Applied Finance},

volume = {23},

number = {5},

pages = {2050033},

abstract = {x},

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@article{craddock_1149,

title = {Lie symmetry methods for local volatility models},

author = {Mark Craddock and Martino Grasselli},

url = {https://www.sciencedirect.com/science/article/abs/pii/S030441491830200X},

year  = {2020},

date = {2020-06-01},

journal = {Stochastic Processes And Their Applications},

volume = {130},

number = {6},

pages = {3802-3841},

abstract = {We investigate PDEs of the form which are associated with the calculation of expectations for a large class of local volatility models. We find nontrivial symmetry groups that can be used to obtain Fourier transforms of fundamental solutions of the PDE. We detail explicit computations in the separable volatility case when , , corresponding to the so called Quadratic Normal Volatility Model. We give financial applications and also show how symmetries can be used to compute first hitting distributions.},

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@article{alfeus_1213,

title = {A Consistent Stochastic Model of the Term Structure of Interest Rates for Multiple Tenors},

author = {Mesias Alfeus and Martino Grasselli and Erik Schlögl},

url = {https://www-sciencedirect-com.devinci.idm.oclc.org/science/article/pii/S0165188920300312},

year  = {2020},

date = {2020-05-01},

journal = {Journal Of Economic Dynamics & Control},

volume = {114},

pages = {103861},

abstract = {Starting from the observation that single-currency swap basis spreads contradict classical arbitrage arguments, we construct a framework where this basis arises due to the presence of ?roll-over risk.? This risk consists of two components: (1) facing a higher credit spread (e.g. due to a credit downgrade) when rolling over short-term borrowing (2) heightened borrowing costs due to an absence of market liquidity. The model simultaneously fits OIS, interest rate swap and basis swap market quotes. Including CDS market quotes allows the two components of roll-over risk to be explicitly separated. This is highly relevant to the current LIBOR transition, illustrating why alternative benchmarks are fundamentally different from the rates they may be replacing.},

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@article{callegaro_550,

title = {Quantization Meets Fourier: a New Technology for Pricing Options},

author = {Gorgia Callegaro and Lucio Fiorin and Martino Grasselli},

url = {https://link.springer.com/article/10.1007%2Fs10479-018-3048-z},

year  = {2019},

date = {2019-11-01},

journal = {Annals Of Operations Research},

volume = {282},

pages = {59-86},

abstract = {In this paper we introduce a novel pricing methodology for a broad class of models for which the characteristic function of the log-asset price can be efficiently computed. The method is based on a new quantization procedure, crucially exploiting for the first time the Fourier transform of the asset process, which fully characterizes the distribution of the log-asset. As opposed to previous quantizations based on Euler (or more sophisticated) discretization schemes, our method reveals to be fast and accurate, to the point that it is possible to calibrate the models on real data. Moreover, our approach allows to price options in multi factor stochastic volatility models including jumps. As a motivating example, we calibrate a Tempered Stable model on market data. This represents the first application of quantization to a pure jump process.},

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@article{deelstra_918,

title = {Explosion time for some Laplace transforms of the Wishart process},

author = {Griselda Deelstra and Martino Grasselli and Christopher Van Weverberg},

url = {https://www.tandfonline.com/doi/full/10.1080/15326349.2019.1578237},

year  = {2019},

date = {2019-03-01},

journal = {Stochastic Models},

volume = {35},

number = {1},

pages = {89-104},

abstract = {In this article, we focus upon a family of matrix valued stochastic processes and study the problem of determining the smallest time such that their Laplace transforms become infinite. In particular, we concentrate upon the class of Wishart processes, which have proved to be very useful in different applications by their ability in describing non-trivial dependence. Thanks to this remarkable property we are able to explain the behavior of the explosion times for the Laplace transforms of the Wishart process and its time integral in terms of the relative importance of the involved factors and their correlations.},

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@article{grasselli_40,

title = {The 4/2 stochastic volatility mode},

author = {Martino Grasselli},

url = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2523635},

year  = {2017},

date = {2017-10-01},

journal = {Mathematical Finance},

volume = {27},

number = {4},

pages = {1013-1034},

abstract = {We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is mathematically and computationally tractable, thereby enabling an efficient pricing procedure. This called for using the Lie symmetries theory for PDEs; doing so allowed us to extend known results on Bessel processes. Finally, we provide an exact simulation scheme for the model; this is useful in view of the numerical applications.},

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@article{callegaro_19,

title = {Pricing via Quantization in Stochastic Volatility Models},

author = {Gorgia Callegaro and Lucio Fiorin and Martino Grasselli},

url = {https://www.tandfonline.com/doi/abs/10.1080/14697688.2016.1255348},

year  = {2017},

date = {2017-06-01},

journal = {Quantitative Finance},

volume = {17},

number = {6},

pages = {p855-p872},

abstract = {In this paper we apply a new methodology based on quantization to price options in stochastic volatility models. This method can be applied to any model for which an Euler scheme is available for the underlying process and it allows for pricing vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process. We apply the methodology to some celebrated stochastic volatility models, including the Stein and Stein (1991) model and the SABR model introduced in Hagan and Woodward (2002). A numerical exercise shows that the pricing of vanillas turns out to be accurate; in addition, when applied to some exotics like equity-volatility options, the quantization-based method overperforms by far the Monte Carlo simulation.},

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@article{deelstra_31,

title = {The Role of the Dependence between Mortality and Interest Rates when pricing Guaranteed Annuity Options},

author = {Griselda Deelstra and Martino Grasselli and Christopher Van Weverberg},

url = {https://www.sciencedirect.com/science/article/pii/S0167668716301664?via%3Dihub},

year  = {2016},

date = {2016-11-01},

journal = {Insurance Mathematics & Economics},

volume = {71},

pages = {p205-p219},

abstract = {In this paper we investigate the consequences on the pricing of insurance contingent claims when we relax the typical independence assumption made in the actuarial literature between mortality risk and interest rate risk. Starting from the Gaussian approach of Liu et al. (2014), we consider some multifactor models for the mortality and interest rates based on more general affine models which remain positive and we derive pricing formulas for insurance contracts like Guaranteed Annuity Options (GAOs). In a Wishart affine model, which allows for a non-trivial dependence between the mortality and the interest rates, we go far beyond the results found in the Gaussian case by Liu et al. (2014), where the value of these insurance contracts can be explained only in terms of the initial pairwise linear correlation.},

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@article{grasselli_42,

title = {A Flexible Spot Multiple-Curve Model},

author = {Martino Grasselli and Giulio Miglietta},

url = {https://www.tandfonline.com/doi/abs/10.1080/14697688.2015.1108521},

year  = {2016},

date = {2016-10-01},

journal = {Quantitative Finance},

volume = {16},

number = {10},

pages = {p1465-p1477},

abstract = {We propose a model for the instantaneous risk-free spot rate and for the spot LIBOR, driven by a time-homogeneous Markovian process. We introduce deterministic time-shifts in order to match any initial term-structure. By doing so, the model automatically becomes an exogenous term-structure model, in the spirit of Brigo and Mercurio (2001) who proposed this approach in the single curve case. A calibration exercise based on real data illustrates the flexibility of our approach for some typical speci fications used in the literature and in the bank industry.},

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pubstate = {published},

tppubtype = {article}

}

@article{caldana_18,

title = {General closed-form basket option pricing bounds},

author = {Ruggero Caldana and Alexandro Gnoatto and Martino Grasselli},

url = {https://www.tandfonline.com/doi/abs/10.1080/14697688.2015.1073854},

year  = {2016},

date = {2016-04-01},

journal = {Quantitative Finance},

volume = {16},

number = {4},

pages = {p535-p554},

abstract = {This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known in closed-form. Moreover, the basket value is not required to be positive. We test our new bounds on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms, hence they do not suffer from the curse of dimensionality. In particular, our new lower bound turns out to be fast and accurate.},

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@article{grasselli_41,

title = {Stochastic Skew and Target Volatility Options},

author = {Martino Grasselli and Jacinto Marabel Romo},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/fut.21720},

year  = {2016},

date = {2016-02-01},

journal = {Journal Of Futures Markets},

volume = {26},

number = {2},

pages = {174-193},

abstract = {Target volatility options (TVO) are a new class of derivatives whose payoff depends on some measure of volatility. These options allow investors to take a joint exposure to the evolution of the underlying asset, as well as to its realized volatility. In equity options markets the slope of the skew is largely independent of the volatility level. A single-factor Heston based volatility model can generate steep skew or flat skew at a given volatility level but cannot generate both for a given parameterization. Since the payoff corresponding to TVO is a function of the joint evolution of the underlying asset and its realized variance, the consideration of stochastic skew is a relevant question for the valuation of TVO.},

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@article{da_fonseca_816,

title = {Analytic Pricing of Volatility- Equity Options within Affine Models: an Efficient Conditioning Technique},

author = {José Da Fonseca and Alexandro Gnoatto and Martino Grasselli},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0167637715001285},

year  = {2015},

date = {2015-06-03},

journal = {Operations Research Letters},

volume = {43},

number = {6},

pages = {601-607},

abstract = {We price for different affine stochastic volatility models some derivatives that recently appeared in the  market. These products  are characterized by payoffs depending on both stock and its volatility. We provide closed-form solution for different products and two multivariate Wishart-based stochastic volatility models. The methodology turns out to be independent of the dimension of the problem. Overall, our results highlight the great flexibility and tractability of Wishart-based stochastic volatility models to develop multivariate extensions of the Heston model.},

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@article{baldeaux_334,

title = {Pricing currency derivatives under the benchmark approach},

author = {Jan Baldeaux and Martino Grasselli and Eckhard Platen},

url = {http://www.sciencedirect.com/science/article/pii/S0378426614003847},

year  = {2015},

date = {2015-04-01},

journal = {Journal Of Banking & Finance},

volume = {53},

pages = {34-48,},

abstract = {This paper considers the realistic modelling of derivative contracts on exchange rates. We propose a stochastic volatility model that recovers not only the typically observed implied volatility smiles and skews for short dated vanilla foreign exchange options but allows one also to price payoffs in foreign currencies, lower than possible under classical risk neutral pricing, in particular, for long dated derivatives. The main reason for this important feature is the strict supermartingale property of benchmarked savings accounts under the real world probability measure, which the calibrated parameters identify under the proposed model. Using a real dataset on vanilla option quotes, we calibrate our model on a triangle of currencies and find that the risk neutral approach fails for the calibrated model, while the benchmark approach still works.},

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@article{chiarella_420,

title = {Pricing Range Notes within Wishart Affine Models},

author = {Carl Chiarella and José Da Fonseca and Martino Grasselli},

url = {http://www.sciencedirect.com/science/article/pii/S0167668714000948},

year  = {2014},

date = {2014-09-01},

journal = {Insurance Mathematics & Economics},

volume = {58},

number = {1},

pages = {193-203},

abstract = {We provide analytic pricing formulas for Fixed and Floating Range Accrual Notes within the multifactor Wishart affine framework which extends significantly the standard affine model. Using estimates for three short rate models, two of which are based on the Wishart process whilst the third one belongs to the standard affine framework, we price these structured products using the FFT methodology. Thanks to the Wishart tractability the hedge ratios are also easily computed. As the models are estimated on the same dataset, our results illustrate how the fit discrepancies (meaning differences in the likelihood functions) between models translate in terms of derivatives pricing errors, and we show that the models can produce different price evolutions for the Range Accrual Notes. The differences can be substantial and underline the importance of model risk both from a static and dynamic perspective. These results are confirmed by an analysis performed at the hedge ratios level.},

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@article{gnoatto_426,

title = {An affine multi-currency model with stochastic volatility and stochastic interest rates},

author = {Alexandro Gnoatto and Martino Grasselli},

url = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2226499},

year  = {2014},

date = {2014-08-01},

journal = {Siam Journal On Financial Mathematics},

volume = {5},

pages = {493-531},

abstract = {We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be efficiently performed through the FFT methodology thanks to the affine property of the model. Our framework is also able to describe many non trivial links between FX rates and interest rates: a calibration exercise highlights the ability of the model to t simultaneously FX implied volatilities while being coherent with interest rate products.},

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@article{da_fonseca_421,

title = {Estimating the Wishart Affi ne Stochastic Correlation Model using the Empirical Characteristic Function},

author = {José Da Fonseca and Martino Grasselli and Florian Ielpo},

url = {https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1054721},

year  = {2014},

date = {2014-06-01},

journal = {Studies In Nonlinear Dynamics And Econometrics},

volume = {18},

number = {3},

pages = {253-289},

abstract = {Abstract: This paper provides the first estimation strategy for the Wishart Affine Stochastic Correlation (WASC) model. We provide elements showing that the use of empirical characteristic function-based estimates is advisable as this function is exponential affine in the WASC case. We use a GMM estimation strategy with a continuum of moment conditions based on the characteristic function. We present the estimation results obtained using a dataset of equity indexes. The WASC model captures most of the known stylized facts associated with financial markets, including leverage and asymmetric correlation effects.},

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tppubtype = {article}

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@article{gnoatto_427,

title = {The explicit Laplace transform for the Wishart process},

author = {Alexandro Gnoatto and Martino Grasselli},

url = {https://www.cambridge.org/core/journals/journal-of-applied-probability/article/explicit-laplace-transform-for-the-wishart-process/96D33CAE7D09562034079343F66FFBCF},

year  = {2014},

date = {2014-05-01},

journal = {Journal Of Applied Probability},

volume = {51},

number = {3},

pages = {640-656},

abstract = {We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral, which extends the original approach of Bru (1991). We compare our methodology with the alternative results given by the variation-of-constants method, the linearization of the matrix Riccati ordinary differential equation, and the Runge-Kutta algorithm. The new formula turns out to be fast and accurate.},

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