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Equivalence of interest rate models and lattice gases
Dan Pirjol
We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure r(t)…
Asymptotic Expansion for the Normal Implied Volatility in Local Volatility Models
Viorel Costeanu, Dan Pirjol
We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the as…
Explosive behavior in a log-normal interest rate model
Dan Pirjol
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions o…
Phase transition in a log-normal Markov functional model
Dan Pirjol
We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct lim…