Term structure modelling for multiple curves with stochastic discontinuities

We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework and provide a fundamental theorem of asset pricing based on NAFLVR. The approach with stochastic discontinuities permits to embed market models directly, unifying seemingly different modelling philosophies. We also develop a tractable class of models, based on affine semimartingales, going beyond the requirement of stochastic continuity

Opažanje niskofrekventnog elektromagnetskog zračenja proizvedenog meteorom

In November 1998, Croatian Physical Society\u27s expedition to Mongolia was undertaken. The goal was to make measurements of the puzzling electrophonic sounds and very low frequency (VLF) radio emission from meteors during the anticipated Leonid meteor storm. During the night of 16/17 November 1998, an extremely high fireball activity of the Leonid meteors occured. During this period, we performed measurements of the VLF radiation from meteors. Here we present a positive signal which consists of a sequence of sharp, short VLF bursts, coincident with the appearance of meteor that was recorded by the video camera. This is the first completely controlled instrumental recording of such an event.Ekspedicija Hrvatskog fizikalnog društvo uputila se u Mongoliju u studenom 1998 radi promatranja očekivane kiše meteora i mjerenja neobičnih elektrofonskih šumova i niskofrekventnog elektromagnetskog zračenja proizvedenog meteorima. U noći 16/17 studenog 1998. došlo je do izrazito pojačane aktivnosti sjajnih meteora Leonida. U tom smo periodu mjerili elektromagnetske valove VLF i istovremeno snimali meteore. Ovdje izvješćujemo o zabilježenom signalu elektromagnetskih valova koji se sastojao od niza kratkotrajnih niskofrekventnih impulsa, koji se pojavio istovremeno s meteorom. Ovo je prvo instrumentalno bilježenje te pojave načinjeno u potpuno kontroliranim uvjetima

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

Explicit Computation of the Post-crisis Spot LIBOR in a Jump-Diffusion Framework

Starting from the worldwide financial crisis originated by the dramatic US economic events happened in 2007, many markets have seen a sudden growth of heterogeneous risk types, spanning from credit ones to liquidity ones. These abrupt changes in fundamentals, have produced the develop of significant spreads between the same interbank rate, e.g. the LIBOR rate, considered at different tenors. In the present chapter, we show how to explicitly compute the post-crisis spot LIBOR at different tenors, taking into account the possibility of jumps in the instantaneous spot rate trajectories, representing, in our setting, the so called OIS short-rate. Such an analysis is based on the intensity approach, where large and sudden movements can be modeled by adding marked point processes to the classical diffusion interest rate framework. Rigorous computations are also provided according with appropriate assumptions on the jumps intensity shape