Curs
2020-2021: Abstracts i Slides
23/06/2021, András Tóbiás, TU Berlin.
SINR percolation for Cox point
processes with random powers
Continuum
percolation is a field in stochastic geometry, where one
considers a random graph based on a stationary point
process in $\mathbb{R}^d$, and the main question is
whether this graph percolates, i.e., whether it contains
an infinite/unbounded connected component.
Signal-to-interference plus noise ratio (SINR) percolation
is an infinite-range dependent variant of continuum
percolation modeling connections in a telecommunication
network. Unlike in earlier works, in our paper the
transmitted signal powers of the devices of the network
are assumed random, i.i.d. and possibly unbounded.
Additionally, we assume that the devices form a stationary
Cox point process, i.e., a Poisson point process with
stationary random intensity measure, in two or higher
dimensions. We present the following main results. First,
under suitable moment conditions on the signal powers and
the intensity measure, there is percolation in the SINR
graph given that the device density is high and
interferences are sufficiently reduced, but not vanishing.
Second, if the interference cancellation factor $\gamma$
and the SINR threshold $\tau$ satisfy $\gamma$ $\geq$
$(2\tau)^{-1}$, then there is no percolation for any
intensity parameter. Third, in the case of a Poisson point
process with constant powers, for any intensity parameter
that is supercritical for the underlying Gilbert graph,
the SINR graph also percolates with some small but
positive interference cancellation factor. The subject of
this talk is joint work with Benedikt Jahnel.
26/05/2021, Frido Rollos, Ortec Finance.
Hedging the forward starting
skew
The
forward start dual volatility swap is introduced, which
can be regarded as the analog for volatility of what the
entropy contract is for variance. Under the pricing
measure it is shown that the difference between the
forward start volatility swap and its dual is
approximately the difference between two specific forward
start implied volatilities. A dynamic replicating strategy
is constructed which allows practitioners to approximately
hedge forward start (dual) volatility swaps and the
forward start skew using two forward start options with
specific strikes.
28/04/2021, Matt Lorig, University of Washington.
Semi-parametric pricing and
hedging of claims on price and volatility
We consider a variety of semi-parametric models for a risky asset $S=\log X$ and show how to robustly price and replicate a variety of path-dependent claims. The semi-parametric models we consider may exhibit both jumps and (possibly non-Markovian) stochastic volatility. Claims may depend on the terminal value of the log price $X$, its realized quadratic variation $[X]$ and barrier-style events. Joint work with Peter Carr and Roger Lee.
24/03/2021, Dragana Radojicic, Serbian Academy of Sciences and Arts.
On a binomial Limit Order Book
model
We introduce a Limit Order Book (LOB) model in discrete time and space, driven by a simple symmetric random walk. We study a basic but non-trivial model of the limit order book where orders get placed with a fixed displacement from the mid-price and get executed whenever the mid-price reaches their level. We define the key quantity, avalanche length, as an avalanche period of trade executions, but allow a small window of size at most $ \varepsilon > 0$ without any execution event. The focus is mainly on the distribution of order avalanches length.
24/02/2021, Jorge León, CINVESTAV.
Stratonovich type integration with respect to fBm with Hurst parameter less than 1/2
In this talk, we introduce a Stratonovich type integral with respect to fBm with Hurst parameter $H\in(0,1/2)$. Then, we study the relation between this integral and the extension of the divergence operator given by León and Nualart, an Itôs formula and the existence of a unique solution to some Stratonovich stochastic differential equations. Towards this end, roughly speaking, we only need to use the norm of the space $L^2(\Omega\times[0,T])$ instead of norm of a Sobolev space given by the Malliavin calculus.
27/01/2021, Raúl Merino, UB.
Option price decomposition for local and stochastic volatility models
In
this seminar, we are going to see a technique to obtain a
decomposition of option prices when there is non-constant
volatility. This technique is a generalization of Alòs
decomposition. The main term in this decomposition is the
Black-Scholes formula plus some corrective terms. We will
see numerical examples of the performance of the
decomposition.
