TY - JOUR
T1 - Explosive behavior in a log-normal interest rate model
AU - Pirjol, Dan
PY - 2013/6
Y1 - 2013/6
N2 - 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 of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, at low and high volatilities, with different qualitative behavior. The two regimes are separated by a sharp transition, which is similar to a phase transition in condensed matter physics. We study the behavior of the model in the large volatility phase, and discuss the implications of the phase transition for the pricing of interest rates derivatives. In the large volatility phase, certain expectation values and convexity adjustments have an explosive behavior. For sufficiently low volatilities the caplet smile is log-normal to a very good approximation, while in the large volatility phase the model develops a non-trivial caplet skew. The phenomenon discussed here imposes thus an upper limit on the volatilities for which the model behaves as intended.
AB - 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 of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, at low and high volatilities, with different qualitative behavior. The two regimes are separated by a sharp transition, which is similar to a phase transition in condensed matter physics. We study the behavior of the model in the large volatility phase, and discuss the implications of the phase transition for the pricing of interest rates derivatives. In the large volatility phase, certain expectation values and convexity adjustments have an explosive behavior. For sufficiently low volatilities the caplet smile is log-normal to a very good approximation, while in the large volatility phase the model develops a non-trivial caplet skew. The phenomenon discussed here imposes thus an upper limit on the volatilities for which the model behaves as intended.
KW - Markov functional model
KW - Short rate models
KW - log-normal interest rate models
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U2 - 10.1142/S0219024913500234
DO - 10.1142/S0219024913500234
M3 - Article
AN - SCOPUS:84880281724
SN - 0219-0249
VL - 16
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
IS - 4
M1 - 1350023
ER -