TY - CHAP
T1 - Stochastic Growth Processes with Exponential Growth Rates
AU - Pirjol, Dan
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - Stochastic growth processes with exponential growth rates are introduced and motivated with examples from stochastic interest rate models. The simplest model of this type is the Black-Derman-Toy (BDT) model, where the interest rate is assumed to follow a geometric Brownian motion. The growth rate of the bank account in the BDT model compounding interest at a stochastic interest rate is computed exactly and shown to have a discontinuous behavior similar to a phase transition.
AB - Stochastic growth processes with exponential growth rates are introduced and motivated with examples from stochastic interest rate models. The simplest model of this type is the Black-Derman-Toy (BDT) model, where the interest rate is assumed to follow a geometric Brownian motion. The growth rate of the bank account in the BDT model compounding interest at a stochastic interest rate is computed exactly and shown to have a discontinuous behavior similar to a phase transition.
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U2 - 10.1007/978-3-031-11143-3_2
DO - 10.1007/978-3-031-11143-3_2
M3 - Chapter
AN - SCOPUS:85137539978
T3 - SpringerBriefs in Applied Sciences and Technology
SP - 19
EP - 37
BT - SpringerBriefs in Applied Sciences and Technology
ER -