arXiv subjects

Sebastian del Bano Rollin

Publications and source records attributed to Sebastian del Bano Rollin.

3 recordsLinked to original sources

arXiv2018

Risk-Neutral Pricing and Hedging of In-Play Football Bets

A risk-neutral valuation framework is developed for pricing and hedging in-play football bets based on modelling scores by independent Poisson processes with constant intensities. The Fundamental Theorems of Asset Pricing are applied to this set-up which enables us to derive novel arbitrage-free valuation formulæ for contracts currently traded in the market. We also describe how to calibrate the model to the market and how trades can be replicated and hedged.

q-fin.TR↗

arXiv2016

Stability of calibration procedures: fractals in the Black-Scholes model

Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has essential singularities at zero and infinity. The singularity at zero reflects the put-call parity. Solving for the implied volatility that reproduces a given market price yields not only a real root, but also infinitely many complex roots in a neighbourhood of the origin. The Newton-Raphson calculation of the complex implied volatility has a chaotic nature described by fractals.

q-fin.MF↗

arXiv1995

The motive of some moduli spaces of vector bundles over a curve

We study the motive of the moduli spaces of semistable rank two vector bundles over an algebraic curve. When the degree is odd the moduli space is a smooth projective variety, we obtain the absolute Hodge motive of this, and in particular the Hodge-Poincare polynomial. When the degree is even the moduli space is a singular projective variety, we compute pure Euler characteristics and show that only two weights can occur in each cohomology group, we also see that its cohomology is pure up to a certain degree. As a by-product we obtain the isogeny type of some intermediate jacobians of the moduli spaces.

alg-geom↗