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# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Pricing of Discretely Monitored Barrier Options - Improvement of an Approximation Formula

and Ögren, Mikael LU (2014) In Master's Theses in Mathematical Sciences FMA820 20141
Mathematics (Faculty of Engineering)
Abstract
There are many different methods for pricing discretely monitored barrier options. There is a trade-off, however, between speed and accuracy. The players on the financial markets would of course ideally want a method which is both exact and returns a price instantaneously.
In this thesis we start from a fast, but on the other hand somewhat less accurate, approximation formula. It will be referred to as the 0.5826-approximation, and was introduced in 1997 by Broadie,Glasserman and Kou [1]. It is one of the option pricing formulas currently used by SunGard. The idea of the 0.5826-approximation is to use the analytical pricing formula for the corresponding continuously monitored barrier option, and to use an adjusted barrier in that formula... (More)
There are many different methods for pricing discretely monitored barrier options. There is a trade-off, however, between speed and accuracy. The players on the financial markets would of course ideally want a method which is both exact and returns a price instantaneously.
In this thesis we start from a fast, but on the other hand somewhat less accurate, approximation formula. It will be referred to as the 0.5826-approximation, and was introduced in 1997 by Broadie,Glasserman and Kou [1]. It is one of the option pricing formulas currently used by SunGard. The idea of the 0.5826-approximation is to use the analytical pricing formula for the corresponding continuously monitored barrier option, and to use an adjusted barrier in that formula to account for the
decreased probability of a barrier hit.
The purpose of this thesis is to improve the 0.5826-approximation for down-and-out call options with barrier less than or equal to the strike, and in particular to mitigate two problems. (Less)
Please use this url to cite or link to this publication:
author
and Ögren, Mikael LU
supervisor
organization
course
FMA820 20141
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Barrier Option, Approximation Formula, Discretely Monitored
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMA-3061-2014
ISSN
1404-6342
other publication id
2014:E29
language
English
id
4462110
date added to LUP
2014-06-26 11:53:21
date last changed
2014-07-04 13:48:11
```@misc{4462110,
abstract     = {There are many different methods for pricing discretely monitored barrier options. There is a trade-off, however, between speed and accuracy. The players on the financial markets would of course ideally want a method which is both exact and returns a price instantaneously.
In this thesis we start from a fast, but on the other hand somewhat less accurate, approximation formula. It will be referred to as the 0.5826-approximation, and was introduced in 1997 by Broadie,Glasserman and Kou [1]. It is one of the option pricing formulas currently used by SunGard. The idea of the 0.5826-approximation is to use the analytical pricing formula for the corresponding continuously monitored barrier option, and to use an adjusted barrier in that formula to account for the
decreased probability of a barrier hit.
The purpose of this thesis is to improve the 0.5826-approximation for down-and-out call options with barrier less than or equal to the strike, and in particular to mitigate two problems.},
author       = {Andersson, Filip and Ögren, Mikael},
issn         = {1404-6342},
keyword      = {Barrier Option,Approximation Formula,Discretely Monitored},
language     = {eng},
note         = {Student Paper},
series       = {Master's Theses in Mathematical Sciences},
title        = {Pricing of Discretely Monitored Barrier Options - Improvement of an Approximation Formula},
year         = {2014},
}

```