Sometimes interest rates fluctuate a lot, sometimes not so much. A standard reference for stochastic volatility interest rates models is Longstaff, Francis and Eduardo Schwartz (1992) Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model, Journal of Finance, Vol. and Jesper Lund (1997), Estimating continuous-time stochastic volatility models of the short-term interest rate, Journal of Econometrics, Vol 77(2), pp. The Longstaff-Schwartz model is a special case of the general multi-dimensional affine factor models. "Models are affine if and only if drift and sigma^2 are affine. Empirical evidence is presented in Andersen, Torben G.

Sometimes interest rates fluctuate a lot, sometimes not so much. A standard reference for stochastic volatility interest rates models is Longstaff, Francis and Eduardo Schwartz (1992) Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model, Journal of Finance, Vol. and Jesper Lund (1997), Estimating continuous-time stochastic volatility models of the short-term interest rate, Journal of Econometrics, Vol 77(2), pp. The Longstaff-Schwartz model is a special case of the general multi-dimensional affine factor models. "Models are affine if and only if drift and sigma^2 are affine. Empirical evidence is presented in Andersen, Torben G.

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Pricing American Options by Monte Carlo Simulation.

(Despite what one might think, there no connection (or is there?

Well-definedness of the problem: Bensoussan (1984), Karatzas (1989), Myneni (1992).

Even in complete(ly) discrete models (as for instance I&F-teori) American securities usually aren't rigorously defined & analyzed (there's no need to because "it's obvious").

They "simply" make a statistical model to fit/predict outcomes of football matches & compares to (mis)quoted odds. Well, you can probably find a lot on the web (try some Google-searches), but I might be able to get my hands on "some of the really good stuff" through my connections with Betbrain.

The technology boom of the past couple of decades has given the average trader access to a much wider range of financial products than ever before.

The article Andersen, Leif, Jesper Andreasen, and David Eliezer, (2002), "Static Replication of Barrier Options: Some General Results , Journal of Computational Finance, 5, 1-25, is "the full Monty" within a PDE-framework: Rebates, interest rates and dividends, general knock-out regions, state and time dependent volatility.

Light numerics will get you a long way with this topic (at least if you stay away from that last article).

The real reason is of course that betting markets are fun. Ziemba "Efficiency of Sports and Lottery Betting Markets", Chapter 18 in Jarrow et al. This is the exact opposite of how things usually work in financial markets, where low risk means low expected return , while very risky (in some sense) investments must have a high expected rate of return.

(If you don't think so, then this is not the topic for you). There is an obvious explanation: Agents in betting markets are risk-lovers, not risk-averse -- why else would they enter the market at all?

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