TY - GEN
T1 - Explosive behavior in the black–derman–toy model
AU - Pirjol, Dan
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - We consider the simulation of the Black–Derman–Toy (BDT) model with log-normally distributed rates in the spot measure, in discrete time and with a continuous state variable. We note an explosive behavior in the Eurodollar futures convexity adjustment at a critical value of the volatility, which depends on maturity, rate tenor, and simulation time step size. In the limit of a very small time step, this singularity appears for any volatility, and reproduces the Hogan–Weintraub singularity, which is generic for short-rate interest rate models with lognormally distributed rates. The singular behavior arises from a region in the state space which is usually truncated off in finite difference and tree methods, or is very poorly sampled in Monte Carlo methods, and thus is not observed under usual simulation methods.
AB - We consider the simulation of the Black–Derman–Toy (BDT) model with log-normally distributed rates in the spot measure, in discrete time and with a continuous state variable. We note an explosive behavior in the Eurodollar futures convexity adjustment at a critical value of the volatility, which depends on maturity, rate tenor, and simulation time step size. In the limit of a very small time step, this singularity appears for any volatility, and reproduces the Hogan–Weintraub singularity, which is generic for short-rate interest rate models with lognormally distributed rates. The singular behavior arises from a region in the state space which is usually truncated off in finite difference and tree methods, or is very poorly sampled in Monte Carlo methods, and thus is not observed under usual simulation methods.
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U2 - 10.1007/978-3-319-12307-3_52
DO - 10.1007/978-3-319-12307-3_52
M3 - Conference contribution
AN - SCOPUS:84951139654
SN - 9783319123066
SN - 9783319123066
T3 - Springer Proceedings in Mathematics and Statistics
SP - 361
EP - 366
BT - Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science
A2 - Makarov, Roman N.
A2 - Melnik, Roderick V. N.
A2 - Kotsireas, Ilias S.
A2 - Shodiev, Hasan
A2 - Cojocaru, Monica G.
A2 - Cojocaru, Monica G.
A2 - Makarov, Roman N.
A2 - Melnik, Roderick V. N.
A2 - Kotsireas, Ilias S.
A2 - Shodiev, Hasan
T2 - International Conference on Applied Mathematics, Modelling and Computational Science, AMMCS 2013
Y2 - 26 August 2013 through 30 August 2013
ER -