TY - JOUR
T1 - Eurodollar futures pricing in log-normal interest rate models in discrete time
AU - Pirjol, Dan
N1 - Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2016/11/1
Y1 - 2016/11/1
N2 - We demonstrate the appearance of explosions in three quantities in interest rate models with log-normally distributed rates in discrete time. (1) The expectation of the money market account in the Black, Derman, Toy model, (2) the prices of Eurodollar futures contracts in a model with log-normally distributed rates in the terminal measure and (3) the prices of Eurodollar futures contracts in the one-factor log-normal Libor market model (LMM). We derive exact upper and lower bounds on the prices and on the standard deviation of the Monte Carlo pricing of Eurodollar futures in the one factor log-normal Libor market model. These bounds explode at a non-zero value of volatility, and thus imply a limitation on the applicability of the LMM and on its Monte Carlo simulation to sufficiently low volatilities.
AB - We demonstrate the appearance of explosions in three quantities in interest rate models with log-normally distributed rates in discrete time. (1) The expectation of the money market account in the Black, Derman, Toy model, (2) the prices of Eurodollar futures contracts in a model with log-normally distributed rates in the terminal measure and (3) the prices of Eurodollar futures contracts in the one-factor log-normal Libor market model (LMM). We derive exact upper and lower bounds on the prices and on the standard deviation of the Monte Carlo pricing of Eurodollar futures in the one factor log-normal Libor market model. These bounds explode at a non-zero value of volatility, and thus imply a limitation on the applicability of the LMM and on its Monte Carlo simulation to sufficiently low volatilities.
KW - Eurodollar futures
KW - Interest rate models
KW - Libor market model
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U2 - 10.1080/1350486X.2017.1297727
DO - 10.1080/1350486X.2017.1297727
M3 - Article
AN - SCOPUS:85016134225
SN - 1350-486X
VL - 23
SP - 445
EP - 464
JO - Applied Mathematical Finance
JF - Applied Mathematical Finance
IS - 6
ER -