A Reduced-Form Stochastic Intensity Model of Timing Prediction Markets
(2026) In Master's Theses in Mathematical Sciences MASM02 20261Mathematical Statistics
- Abstract
- In prediction markets actors trade contracts whose payout is linked to the occurrence of real-world events. Markets based on questions of the type "Will event A occur before time T?" are particularly interesting in geopolitical contexts, but are understudied in comparison to standard election-style contracts. I present, to the best of my knowledge, the first pricing model for this type of market, based on a reduced-form framework. Suppose that the underlying event arrives with a doubly stochastic Poisson process, driven by a random intensity. The corresponding prediction market price is then related to the process' first-arrival distribution. This allows for tractable pricing equations for a range of reasonable intensity dynamics. I study,... (More)
- In prediction markets actors trade contracts whose payout is linked to the occurrence of real-world events. Markets based on questions of the type "Will event A occur before time T?" are particularly interesting in geopolitical contexts, but are understudied in comparison to standard election-style contracts. I present, to the best of my knowledge, the first pricing model for this type of market, based on a reduced-form framework. Suppose that the underlying event arrives with a doubly stochastic Poisson process, driven by a random intensity. The corresponding prediction market price is then related to the process' first-arrival distribution. This allows for tractable pricing equations for a range of reasonable intensity dynamics. I study, in particular, a Cox-Ingersoll-Ross specification with compound Poisson jumps, and propose a Kalman-filter-based quasi-maximum likelihood estimator of the model parameters. Future prices are forecasted using a Monte Carlo procedure. We can also compute the model-implied probability of the underlying event having occurred by any specified date. Such a model enables sophisticated risk management and market making strategies, which have previously been unfeasible for this type of prediction market. (Less)
- Popular Abstract
- In prediction markets participants trade financial contracts which pay out a fixed amount—typically one dollar—to the holder if some real-world event occurs. The most traded contracts have historically been bets on which candidate will win a U.S. presidential election. In these markets the price of a contract can be interpreted as an estimate of the probability of the underlying event occurring. For example, if you think that there is a 30 % chance of occurrence, then the most you should rationally be willing to pay for the corresponding one dollar contract is 30 cents. In this thesis I study a less common form of prediction market based on questions of the type "Will event A occur before time T?" The probability of the answer being yes... (More)
- In prediction markets participants trade financial contracts which pay out a fixed amount—typically one dollar—to the holder if some real-world event occurs. The most traded contracts have historically been bets on which candidate will win a U.S. presidential election. In these markets the price of a contract can be interpreted as an estimate of the probability of the underlying event occurring. For example, if you think that there is a 30 % chance of occurrence, then the most you should rationally be willing to pay for the corresponding one dollar contract is 30 cents. In this thesis I study a less common form of prediction market based on questions of the type "Will event A occur before time T?" The probability of the answer being yes goes to zero close to the end date T, and with it the contract price. This is qualitatively different from the behaviour of election-style markets, where there is typically a lot of uncertainty left near the end. I call the former type timing markets. They are particularly interesting in geopolitical contexts; a series of markets with various end dates have been run, e.g., on the ousting of Ayatollah Khamenei.
I present the first, to the best of my knowledge, mathematical model of timing market prices and of how they evolve. Consider the probability that an underlying event will occur in the next (infinitesimally) small interval of time; this probability is called the intensity. By assuming that it changes randomly over time in specific ways I am able to compute the implied probability that the underlying event will occur before the market's end date T. This corresponds to the market price of the associated timing prediction contract. The model I present is able to make forecasts for future market prices. It can also be used to estimate the probability that the event will have occurred by any specified date, not just the end date T. By studying how good the model's predictions are on real timing markets, I conclude that although the model as presented is flawed, the proposed modeling framework is promising. A good model of this type, towards the development of which I have made a first contribution, could enable traders in timing prediction markets to employ sophisticated risk management strategies that have previously been infeasible. This is necessary if they are to approach the maturity of traditional financial markets. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/student-papers/record/9229202
- author
- Göransson-Gaspar, Erik LU
- supervisor
- organization
- course
- MASM02 20261
- year
- 2026
- type
- H2 - Master's Degree (Two Years)
- subject
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUNFMS-3141-2026
- ISSN
- 1404-6342
- other publication id
- 2026:E34
- language
- English
- id
- 9229202
- date added to LUP
- 2026-06-05 17:46:34
- date last changed
- 2026-06-05 17:46:34
@misc{9229202,
abstract = {{In prediction markets actors trade contracts whose payout is linked to the occurrence of real-world events. Markets based on questions of the type "Will event A occur before time T?" are particularly interesting in geopolitical contexts, but are understudied in comparison to standard election-style contracts. I present, to the best of my knowledge, the first pricing model for this type of market, based on a reduced-form framework. Suppose that the underlying event arrives with a doubly stochastic Poisson process, driven by a random intensity. The corresponding prediction market price is then related to the process' first-arrival distribution. This allows for tractable pricing equations for a range of reasonable intensity dynamics. I study, in particular, a Cox-Ingersoll-Ross specification with compound Poisson jumps, and propose a Kalman-filter-based quasi-maximum likelihood estimator of the model parameters. Future prices are forecasted using a Monte Carlo procedure. We can also compute the model-implied probability of the underlying event having occurred by any specified date. Such a model enables sophisticated risk management and market making strategies, which have previously been unfeasible for this type of prediction market.}},
author = {{Göransson-Gaspar, Erik}},
issn = {{1404-6342}},
language = {{eng}},
note = {{Student Paper}},
series = {{Master's Theses in Mathematical Sciences}},
title = {{A Reduced-Form Stochastic Intensity Model of Timing Prediction Markets}},
year = {{2026}},
}