Multivariate Asset Models Using Levy Processes and Applications

In this paper we propose a multivariate asset model based on L´evy processes for pricing of products written on more than one underlying asset. Our construction is based on a two factor representation of the dynamics of the asset log-returns. We investigate the properties of the model and introduce a multivariate generalization of some processes which are quite common in financial applications, such as subordinated Brownian motions, jump diffusion processes and time changed L´evy processes. Finally, we explore the issue of model calibration for the proposed setting and illustrate its robustness on a number of numerical examples

The impact of longevity and investment risk on a portfolio of life insurance liabilities

In this paper we assess the joint impact of biometric and financial risk on the market valuation of life insurance liabilities. We consider a stylized, contingent claim based model of a life insurance company issuing participating contracts and subject to default risk, as pioneered by Briys and de Varenne (Geneva Pap Risk Insur Theory 19(1):53–72, 1994, J Risk Insur 64(4):673–694, 1997), and build on their model by explicitly introducing biometric risk and its components, namely diversifiable and systematic risk. The contracts considered include pure endowments, deferred whole life annuities and guaranteed annuity options. Our results stress the predominance of systematic over diversifiable risk in determining fair participation rates. We investigate the interaction of contract design, market regimes and mortality assumptions, and show that, particularly for lifelong benefits, the choice of the participation rate must be very conservative if longevity improvements are foreseeable

A note on the alpha-quantile option

In this communication, we discuss some properties of a class of path dependent options based on the α-quantiles of Brownian motion. In particular we show that such options are well behaved in relation to standard options and comparatively cheaper than an equivalent class of lookback options

The valuation of guaranteed lifelong withdrawal benefit options in variable annuity contracts and the impact of mortality risk

n light of the growing importance of the variable annuities market, in this paper we introduce a theoretical model for the pricing and valuation of guaranteed lifelong withdrawal benefit (GLWB) options embedded in variable annuity products. As the name suggests, this option offers a lifelong withdrawal guarantee; therefore, there is no limit on the total amount that is withdrawn over the term of the policy because if the account value becomes zero while the insured is still alive, he or she continues to receive the guaranteed amount annually until death. Any remaining account value at the time of death is paid to the beneficiary as a death benefit. We offer a specific framework to value the GLWB option in a market-consistent manner under the hypothesis of a static withdrawal strategy, according to which the withdrawal amount is always equal to the guaranteed amount. The valuation approach is based on the decomposition of the product into living and death benefits. The model makes use of the standard no-arbitrage models of mathematical finance, which extend the Black-Scholes framework to insurance contracts, assuming the fund follows a geometric Brownian motion and the insurance fee is paid, on an ongoing basis, as a proportion of the assets. We develop a sensitivity analysis, which shows how the value of the product varies with the key parameters, including the age of the policyholder at the inception of the contract, the guaranteed rate, the risk-free rate, and the fund volatility. We calculate the fair fee, using Monte Carlo simulations under different scenarios. We give special attention to the impact of mortality risk on the value of the option, using a flexible model of mortality dynamics, which allows for the possible perturbations by mortality shock of the standard mortality tables used by practitioners. Moreover, we evaluate the introduction of roll-up and step-up options and the effect of the decision to delay withdrawing. Empirical analyses are performed, and numerical results are provided

Convertible bond valuation in a jump diffusion setting with stochastic interest rates

This paper proposes an integrated pricing framework for convertible bonds, which comprises firm value evolving as an exponential jump diffusion, correlated stochastic interest rates movements and an efficient numerical pricing scheme. By construction, the proposed stochastic model fits in the framework of affine jump diffusion processes of Duffie et al. [Econometrica, 2000, 68, 1343–1376] with tractable behaviour. We define the firm’s optimal call policy and investigate its impact on the computed convertible bond prices. We illustrate the performance of the numerical scheme and highlight the effects originated by the inclusion of jumps, stochastic interest rates and a non-zero correlation structure between firm value and interest rates

Efficient pricing of ratchet equity-indexed annuities in a variance-gamma economy

In this paper we propose a new method for approximating the price of arithmetic Asian options in a Variance-Gamma (VG) economy, which is then applied to the problem of pricing equityindexed annuity contracts. The proposed procedure is an extension to the case of a VG-based model of the moment-matching method developed by Turnbull and Wakeman and Levy for the pricing of this class of path-dependent options in the traditional Black-Scholes setting. The accuracy of the approximation is analyzed against RQMC estimates for the case of ratchet equityindexed annuities with index averaging

The term structure of implied correlations between S&P and VIX markets

We develop a joint model for the S&P500 and the VIX indices with the aim of extracting forward looking information on the correlation between the two markets. We achieve this by building the model on time changed L´evy processes, deriving closed analytical expressions for relevant quantities directly from the joint characteristic function, and exploiting the market quotes of options on both indices. We perform a piecewise joint calibration to the option prices to ensure the highest level of precision within the limits of the availability of quotes in the dataset and their liquidity. Using the calibrated parameters, we are able to quantify the leverage effect along the term structure of the VIX options and corresponding VIX futures. We illustrate the model using market data on S&P500 options and both futures and options on the VIX

Temporal Lobe Spikes Affect Distant Intrinsic Connectivity Networks

Objective: To evaluate local and distant blood oxygen level dependent (BOLD) signal changes related to interictal epileptiform discharges (IED) in drug-resistant temporal lobe epilepsy (TLE). Methods: Thirty-three TLE patients undergoing EEG–functional Magnetic Resonance Imaging (fMRI) as part of the presurgical workup were consecutively enrolled. First, a single-subject spike-related analysis was performed: (a) to verify the BOLD concordance with the presumed Epileptogenic Zone (EZ); and (b) to investigate the Intrinsic Connectivity Networks (ICN) involvement. Then, a group analysis was performed to search for common BOLD changes in TLE. Results: Interictal epileptiform discharges were recorded in 25 patients and in 19 (58%), a BOLD response was obtained at the single-subject level. In 42% of the cases, BOLD changes were observed in the temporal lobe, although only one patient had a pure concordant finding, with a single fMRI cluster overlapping (and limited to) the EZ identified by anatomo-electro-clinical correlations. In the remaining 58% of the cases, BOLD responses were localized outside the temporal lobe and the presumed EZ. In every patient, with a spike-related fMRI map, at least one ICN appeared to be involved. Four main ICNs were preferentially involved, namely, motor, visual, auditory/motor speech, and the default mode network. At the single-subject level, EEG–fMRI proved to have high specificity (above 65%) in detecting engagement of an ICN and the corresponding ictal/postictal symptom, and good positive predictive value (above 67%) in all networks except the visual one. Finally, in the group analysis of BOLD changes related to IED revealed common activations at the right precentral gyrus, supplementary motor area, and middle cingulate gyrus. Significance: Interictal temporal spikes affect several distant extra-temporal areas, and specifically the motor/premotor cortex. EEG–fMRI in patients with TLE eligible for surgery is recommended not for strictly localizing purposes rather it might be useful to investigate ICNs alterations at the single-subject level

The T.O.S.C.A. Project: Research, Education and Care

Despite recent and exponential improvements in diagnostic- therapeutic pathways, an existing “GAP” has been revealed between the “real world care” and the “optimal care” of patients with chronic heart failure (CHF). We present the T.O.S.CA. Project (Trattamento Ormonale dello Scompenso CArdiaco), an Italian multicenter initiative involving different health care professionals and services aiming to explore the CHF “metabolic pathophysiological model” and to improve the quality of care of HF patients through research and continuing medical education

Can Disruption of Basal Ganglia-Thalamocortical Circuit in Wilson Disease Be Associated with Juvenile Myoclonic Epilepsy Phenotype?

In this paper, we describe the multimodal MRI findings in a patient with Wilson disease and a seizure disorder, characterized by an electroclinical picture resembling juvenile myoclonic epilepsy. The brain structural MRI showed a deposition of ferromagnetic materials in the basal ganglia, with marked hypointensities in T2-weighted images of globus pallidus internus bilaterally. A resting-state fMRI study revealed increased functional connectivity in the patient, compared to control subjects, in the following networks: (1) between the primary motor cortex and several cortical regions, including the secondary somatosensory cortex and (2) between the globus pallidus and the thalamo-frontal network. These findings suggest that globus pallidus alterations, due to metal accumulation, can lead to a reduction in the normal globus pallidus inhibitory tone on the thalamo-(motor)-cortical pathway. This, in turn, can result in hyperconnectivity in the motor cortex circuitry, leading to myoclonus and tonic-clonic seizures. We suppose that, in this patient, Wilson disease generated a ‘lesion model’ of myoclonic epilepsy