76 research outputs found
Derivative pricing for a multi-curve extension of the Gaussian, exponentially quadratic short rate model
The recent financial crisis has led to so-called multi-curve models for the
term structure. Here we study a multi-curve extension of short rate models
where, in addition to the short rate itself, we introduce short rate spreads.
In particular, we consider a Gaussian factor model where the short rate and the
spreads are second order polynomials of Gaussian factor processes. This leads
to an exponentially quadratic model class that is less well known than the
exponentially affine class. In the latter class the factors enter linearly and
for positivity one considers square root factor processes. While the square
root factors in the affine class have more involved distributions, in the
quadratic class the factors remain Gaussian and this leads to various
advantages, in particular for derivative pricing. After some preliminaries on
martingale modeling in the multi-curve setup, we concentrate on pricing of
linear and optional derivatives. For linear derivatives, we exhibit an
adjustment factor that allows one to pass from pre-crisis single curve values
to the corresponding post-crisis multi-curve values
On multicurve models for the term structure
In the context of multi-curve modeling we consider a two-curve setup, with
one curve for discounting (OIS swap curve) and one for generating future cash
flows (LIBOR for a give tenor). Within this context we present an approach for
the clean-valuation pricing of FRAs and CAPs (linear and nonlinear derivatives)
with one of the main goals being also that of exhibiting an "adjustment factor"
when passing from the one-curve to the two-curve setting. The model itself
corresponds to short rate modeling where the short rate and a short rate spread
are driven by affine factors; this allows for correlation between short rate
and short rate spread as well as to exploit the convenient affine structure
methodology. We briefly comment also on the calibration of the model
parameters, including the correlation factor.Comment: 16 page
Epidemic variability in complex networks
We study numerically the variability of the outbreak of diseases on complex
networks. We use a SI model to simulate the disease spreading at short times,
in homogeneous and in scale-free networks. In both cases, we study the effect
of initial conditions on the epidemic's dynamics and its variability. The
results display a time regime during which the prevalence exhibits a large
sensitivity to noise. We also investigate the dependence of the infection time
on nodes' degree and distance to the seed. In particular, we show that the
infection time of hubs have large fluctuations which limit their reliability as
early-detection stations. Finally, we discuss the effect of the multiplicity of
shortest paths between two nodes on the infection time. Furthermore, we
demonstrate that the existence of even longer paths reduces the average
infection time. These different results could be of use for the design of
time-dependent containment strategies
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Convexity Adjustment for Constant maturity Swaps in a Multi-Curve Framework
In this paper we propose a double curving setup with distinct forward and discount curves to price constant maturity swaps (CMS). Using separate curves for discounting and forwarding, we develop a new convexity adjustment, by departing from the restrictive assumption of a flat term structure, and expand our setting to incorporate the more realistic and even challenging case of term structure tilts. We calibrate CMS spreads to market data and numerically compare our adjustments against the Black and SABR (stochastic alpha beta rho) CMS adjustments widely used in the market. Our analysis suggests that the proposed convexity adjustment is significantly larger compared to the Black and SABR adjustments and offers a consistent and robust valuation of CMS spreads across different market conditions
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