1,721,108 research outputs found
Bond price and impulse response function for the Balduzzi, Das, Foresi and Sundaram (1996) model
No full textIn this paper, we analyse the Affine Term Structure Model (ATSM) proposed by Balduzzi, Das, Foresi and Sundaram (BDFS, 1996) and provide the closed-form expression of the bond price. In addition, we extend the notion of Impulse Response Function to the class of ATSM. We show that it is closely related to the duration measure, and we compute it explicitly in the BDFS model. © Banca Monte dei Paschi di Siena SpA, 2004
Long versus short time scales: the rough dilemma and beyond
No full textUsing 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
Vix versus vxx: a joint analytical framework
No full textWe propose a framework for modeling in a consistent manner the VIX index and the VXX, an exchange-traded note written on the VIX. Our study enables to link the properties of VXX to those of the VIX in a tractable way. In particular, we quantify the systematic loss observed empirically for VXX when the VIX futures term-structure is in contango and we derive option prices, implied volatilities and skews of VXX from those of VIX in infinitesimal developments. We also perform a calibration on real data which highlights the flexibility of our model in fitting the futures and the vanilla options market of VIX and VXX. Our framework can be used to model other exchange-traded notes on the VIX as well as any market where exchange-traded notes have been introduced on a reference index, hence providing tools to better anticipate and quantify systematic behavior of an exchange-traded note with respect to the underlying index
THE EXPLICIT LAPLACE TRANSFORM FOR THE WISHART PROCESS
No full textWe 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
A PHASE-FIELD SYSTEM ARISING FROM MULTISCALE MODELING OF THROMBUS BIOMECHANICS IN BLOOD VESSELS: LOCAL WELL-POSEDNESS IN DIMENSION TWO
No full textWe consider a phase-field model which describes the interactions between the blood flow and the thrombus. The latter is supposed to be a viscoelastic material. The potential describing the cohesive energy of the mixture is assumed to be of Flory-Huggins type (i.e. logarithmic). This ensures the boundedness from below of the dissipation energy. In the two dimensional case, we prove the local (in time) existence and uniqueness of a strong solution, provided that the two viscosities of the pure fluid phases are close enough. We also show that the order parameter remains strictly separated from the pure phases if it is so at the initial time
“Creating the (School’s) Future. Imagination, Prediction and Argumentative Competence”.
Full text linkA policyholder's indifference valuation for the guaranteed annuity option
No full textGuaranteed annuity options belong to the class of long term guarantees that insurance companies may offer to their policy- holders. They were very common in U.S. tax-sheltered plans and U.K. retirement savings. These options may represent a very valuable liability for the insurer, being exposed to two dif- ferent sources of randomness: the future interest rates and the future mortality (hazard) rates. Both financial and actuarial ap- proaches have been used to evaluate and describe the nature of such options. In the present work, we present an indifference valuation method for the guaranteed annuity option, from the policyholder’s point of view. In a setting where interest rates are constant, we find an explicit solution for the indifference problem, where the individual is described by a power (instan- taneous) utility function. In this setting, we compare two strate- gies at the time of conversion, and two strategies at the moment when the policy is purchased. In the former, we assume that if the annuitant does not exercise the option, first she withdraws her policy’s accumulated funds, and then seeks to solve a stan- dard Merton’s problem, under an infinite time horizon setting. In the latter strategy, we compare the agent’s expected utility associated to a policy that embeds a guaranteed annuity option, and a policy that does not embed such an option. In order to accumulate the retirement funds, we assume in both cases a pure premium paid at a constant continuous stream. Regard- ing the optimal strategy, we are able to derive explicit solutions for a class of problems where finite horizon, bequest motive and power consumption utility are considered. We conclude the present framework by allowing the agent to earn a constant labor income. As expected, since the income is non-random, we find that the indifference valuation of implicit guaranteed annuity option is not influenced by this richer setting
A policyholder's utility indifference valuation model for the guaranteed annuity option
No full textInsurance companies often include very long-term guaran- tees in participating life insurance products, which can turn out to be very valuable. Under a guaranteed annuity options (g.a.o.), the insurer guarantees to convert a policyholder’s accumulated funds to a life annuity at a fixed rated when the policy matures. Both financial and actuarial approaches have been used to valuate of such options. In the present work, we present an indifference valuation model for the guaranteed an- nuity option. We are interested in the additional lump sum that the policyholder is willing to pay in order to have the option to convert the accumulated funds into a lifelong annuity at a guaranteed rate
Pricing the option to annuitise using the principle of equivalent utility
No full textConvegno AMASES - Trieste
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