### Abstract

We study the short time behavior of the early exercise boundary for American style put options in the Black Scholes theory. We develop an asymptotic expansion which shows that the simple lower bound of Barles et al. is a more accurate approximation to the actual boundary than the more complex upper bound. Our expansion is obtained through iteration using a boundary integral equation. This integral equation is derived from the time derivative of the option value function, which closely resembles the classical Stefan free boundary value problem for melting ice. Our analytical results are supported by numerical computations designed for very short times.

Original language | English (US) |
---|---|

Pages (from-to) | 1823-1838 |

Number of pages | 16 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 62 |

Issue number | 5 |

DOIs | |

State | Published - May 2002 |

### Fingerprint

### Keywords

- American put
- Black-Scholes
- Free boundary

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*62*(5), 1823-1838. https://doi.org/10.1137/S0036139900378293

**On the early exercise boundary of the American put option.** / Goodman, Jonathan; Ostrov, Daniel N.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 62, no. 5, pp. 1823-1838. https://doi.org/10.1137/S0036139900378293

}

TY - JOUR

T1 - On the early exercise boundary of the American put option

AU - Goodman, Jonathan

AU - Ostrov, Daniel N.

PY - 2002/5

Y1 - 2002/5

N2 - We study the short time behavior of the early exercise boundary for American style put options in the Black Scholes theory. We develop an asymptotic expansion which shows that the simple lower bound of Barles et al. is a more accurate approximation to the actual boundary than the more complex upper bound. Our expansion is obtained through iteration using a boundary integral equation. This integral equation is derived from the time derivative of the option value function, which closely resembles the classical Stefan free boundary value problem for melting ice. Our analytical results are supported by numerical computations designed for very short times.

AB - We study the short time behavior of the early exercise boundary for American style put options in the Black Scholes theory. We develop an asymptotic expansion which shows that the simple lower bound of Barles et al. is a more accurate approximation to the actual boundary than the more complex upper bound. Our expansion is obtained through iteration using a boundary integral equation. This integral equation is derived from the time derivative of the option value function, which closely resembles the classical Stefan free boundary value problem for melting ice. Our analytical results are supported by numerical computations designed for very short times.

KW - American put

KW - Black-Scholes

KW - Free boundary

UR - http://www.scopus.com/inward/record.url?scp=0036588758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036588758&partnerID=8YFLogxK

U2 - 10.1137/S0036139900378293

DO - 10.1137/S0036139900378293

M3 - Article

AN - SCOPUS:0036588758

VL - 62

SP - 1823

EP - 1838

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 5

ER -