### Abstract

In this article, we shall prove an integration by parts (IBP) type formula for stopping times. In order to obtain the formula, we will first construct a process which works as if it is an “alarm clock” telling us whether the stopping times are already achieved or not. Then, we shall use the Girsanov theorem. Applications of the formula to the numerical computation of the risk called the delta for options depending on the stopping times will be also considered and show the gain of efficiency compared with a classical method.

Original language | English |
---|---|

Pages (from-to) | 751-773 |

Number of pages | 23 |

Journal | Methodology and Computing in Applied Probability |

Volume | 19 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2017 Sep 1 |

Externally published | Yes |

### Keywords

- American option
- Greeks
- Integration by parts
- Stochastic differential equation
- Stopping time

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)

### Cite this

**An Integration by Parts Type Formula for Stopping Times and its Application.** / Nakatsu, Tomonori.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An Integration by Parts Type Formula for Stopping Times and its Application

AU - Nakatsu, Tomonori

PY - 2017/9/1

Y1 - 2017/9/1

N2 - In this article, we shall prove an integration by parts (IBP) type formula for stopping times. In order to obtain the formula, we will first construct a process which works as if it is an “alarm clock” telling us whether the stopping times are already achieved or not. Then, we shall use the Girsanov theorem. Applications of the formula to the numerical computation of the risk called the delta for options depending on the stopping times will be also considered and show the gain of efficiency compared with a classical method.

AB - In this article, we shall prove an integration by parts (IBP) type formula for stopping times. In order to obtain the formula, we will first construct a process which works as if it is an “alarm clock” telling us whether the stopping times are already achieved or not. Then, we shall use the Girsanov theorem. Applications of the formula to the numerical computation of the risk called the delta for options depending on the stopping times will be also considered and show the gain of efficiency compared with a classical method.

KW - American option

KW - Greeks

KW - Integration by parts

KW - Stochastic differential equation

KW - Stopping time

UR - http://www.scopus.com/inward/record.url?scp=84983470035&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983470035&partnerID=8YFLogxK

U2 - 10.1007/s11009-016-9512-9

DO - 10.1007/s11009-016-9512-9

M3 - Article

AN - SCOPUS:84983470035

VL - 19

SP - 751

EP - 773

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

IS - 3

ER -