Risk-neutral Derivation of In-play Bet Prices by Modeling Football Matches: A Weibull Point Process Approach
Author
Andersen, Morten
Term
4. term
Education
Publication year
2020
Submitted on
2020-06-02
Pages
99
Abstract
Dette speciale undersøger, om live (in-play) fodbold-bets kan prissættes med en risikoneutral tilgang kendt fra finansielle markeder. Vi modellerer, hvornår mål falder, med Weibull-baserede punktprocesser – statistiske modeller hvor ventetiden mellem mål følger en fleksibel fordeling – og bygger derpå en risikoneutral værdiansættelsesramme. Derefter tester vi, om de fundamentale sætninger for prisdannelse (Fundamental Theorems of Asset Pricing), som forbinder fravær af arbitrage med et risikoneutralt sandsynlighedsmål, kan beskrive betting-markeder ved at kalibrere modelpriser til odds fra en spilbørs. Først vurderer vi egnetheden af to mål-tidsmodeller, Weibull-processen og Weibull-fornyelsesprocessen, og sammenholder deres afledte priser med observerede markedspriser. Begge modeller giver lovende resultater inden for deres begrænsninger, men vi finder ikke endegyldig evidens for, at et risikoneutralt sandsynlighedsmål findes i disse markedsmodeller. Alligevel peger resultaterne på lovende veje til videre arbejde med at anvende prisdannelsesteori i live fodbold-betting.
This thesis examines whether live (in-play) football bets can be priced using a risk-neutral approach borrowed from financial markets. We model when goals occur with Weibull-based point processes—statistical models in which the waiting time between goals follows a flexible distribution—and use them to build a risk-neutral valuation framework. We then ask whether the Fundamental Theorems of Asset Pricing, which link no-arbitrage markets to a risk-neutral probability, apply to betting markets by calibrating model prices to odds from a betting exchange. We first assess the suitability of two goal-timing models, the Weibull process and the Weibull renewal process, and then compare their implied prices with observed market prices. Both models perform promisingly within their limitations, but we do not find conclusive evidence that a risk-neutral measure exists in these market models. Even so, our results point to promising directions for further applying asset-pricing theory to in-play football betting.
[This abstract was generated with the help of AI]
Keywords
Risk-neutral ; Football ; Betting ; Pricing ; Weibull ; Point process ; Counting process
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