Optimal Investment in Markets with Over and Under-Reaction to Information

Callegaro, Giorgia; Gaïgi, M’hamed; Scotti, Simone; Sgarra, Carlo

doi:10.2139/ssrn.2627089

Cited by 3 publications

(5 citation statements)

References 42 publications

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“…Since the model is affine, cumulants can be computed analytically, for this purpose, we adapt Probability density functions of X T and implied volatilities for short and long maturities for the calibrated parameters in Table 1 (Set A) the procedure outlined in Feunou and Okou [27]. According to Fang and Oosterlee [26], if L = 10, (14) gives a truncation error around 10 −12 , which is negligible for our purposes. Given European options prices, the corresponding implied volatility can be computed by inverting the Black-Scholes formula.…”

Section: European Option Pricing and Calibrationmentioning

confidence: 99%

“…Since the sample starts in a period of mild volatility we can reasonably assume that the Hawkes intensity, at this time, is close to its minimal level, which we denote by . The jumps are detected as the larger positive fluctuations using the algorithm detailed in Callegaro et al [ 14 ].…”

Section: Clusters In Vix: Stylized Factsmentioning

confidence: 99%

“…We can reproduce this effect with only positive jumps in VIX and an exponential mean-reversion speed. Moreover, the method adopted to identify jumps is unable to detect relatively small jumps (see [ 14 ]). In particular, jumps smaller than three standard deviations of the other increments are classified as usual Brownian noise.…”

Section: Clusters In Vix: Stylized Factsmentioning

confidence: 99%

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A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process

Bernis¹,

Brignone

Scotti

et al. 2021

Math Finan Econ

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We propose an extension of the $$\Gamma $$ Γ -OU Barndorff-Nielsen and Shephard model taking into account jump clustering phenomena. We assume that the intensity process of the Hawkes driver coincides, up to a constant, with the variance process. By applying the theory of continuous-state branching processes with immigration, we prove existence and uniqueness of strong solutions of the SDE governing the asset price dynamics. We propose a measure change of self-exciting Esscher type in order to describe the relation between the risk-neutral and the historical dynamics, showing that the $$\Gamma $$ Γ -OU Hawkes framework is stable under this probability change. By exploiting the affine features of the model we provide an explicit form for the Laplace transform of the asset log-return, for its quadratic variation and for the ergodic distribution of the variance process. We show that the proposed model exhibits a larger flexibility in comparison with the $$\Gamma $$ Γ -OU model, in spite of the same number of parameters required. We calibrate the model on market vanilla option prices via characteristic function inversion techniques, we study the price sensitivities and propose an exact simulation scheme. The main financial achievement is that implied volatility of options written on VIX is upward shaped due to the self-exciting property of Hawkes processes, in contrast with the usual downward slope exhibited by the $$\Gamma $$ Γ -OU Barndorff-Nielsen and Shephard model.

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Section: European Option Pricing and Calibrationmentioning

confidence: 99%

Section: Clusters In Vix: Stylized Factsmentioning

confidence: 99%

Section: Clusters In Vix: Stylized Factsmentioning

confidence: 99%

See 1 more Smart Citation

A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process

Bernis¹,

Brignone

Scotti

et al. 2021

Math Finan Econ

Self Cite

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“…In the same spirit of Callegaro el al. [9], we identify jumps using an iterated re-weighted least squared technique. The daily data span the period between April 1, 2004 and December 31, 2015.…”

Section: Jump Detection and Cluster Identificationmentioning

confidence: 99%

A branching process approach to power markets

Jiao

Scotti

et al. 2019

Energy Economics

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We propose and investigate a market model for power prices, including most basic features exhibited by previous models and taking into account self-exciting properties. The model proposed extends Hawkes-type models by introducing a two-fold integral representation property. A Random Field approach was already exploited by Barndorff-Nielsen et al., who adopted the Ambit Field framework for describing the power price dynamics. The novelty contained in our approach consists in combining the basic features of both Branching Processes and Random Fields in order to get a realistic and parsimonious model setting. We shall provide some closed-form evaluation formulae for forward contracts. We discuss the risk premium behavior, by pointing out that in the present framework, a very realistic description arises. We outline a possible methodology for parameters estimation. We illustrate by graphical representation the main achievements of this approach.

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“…A few papers consider mixed-type information (see e.g. Callegaro et al [10] and Frey and Schmidt [35], among others). In our paper, we deal with a more general setting with a two-dimensional observation process allowing jumps, for which known results cannot be invoked.…”

Section: Introductionmentioning

confidence: 99%

Optimal reduction of public debt under partial observation of the economic growth

2020

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We consider a government that aims at reducing the debt-to-(gross domestic product) (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic conditions. The government’s criterion is to minimise the sum of the total expected costs of holding debt and of debt reduction policies. We model this problem as a singular stochastic control problem under partial observation. The contribution of the paper is twofold. Firstly, we provide a general formulation of the model in which the level of the debt-to-GDP ratio and the value of the macroeconomic indicator evolve as a diffusion and a jump-diffusion, respectively, with coefficients depending on the regimes of the economy. The latter are described through a finite-state continuous-time Markov chain. We reduce the original problem via filtering techniques to an equivalent one with full information (the so-called separated problem), and we provide a general verification result in terms of a related optimal stopping problem under full information. Secondly, we specialise to a case study in which the economy faces only two regimes and the macroeconomic indicator has a suitable diffusive dynamics. In this setting, we provide the optimal debt reduction policy. This is given in terms of the continuous free boundary arising in an auxiliary fully two-dimensional optimal stopping problem.

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Optimal Investment in Markets with Over and Under-Reaction to Information

Cited by 3 publications

References 42 publications

A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process

A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process

A branching process approach to power markets

Optimal reduction of public debt under partial observation of the economic growth

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