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Pricing Timer Options under Jump-Diffusion Processes

Müller, Janis (2014) MASM01 20141
Mathematical Statistics
Abstract (Swedish)
Timer options are relatively new exotic options with the feature that they expire as soon as the
accumulated realized variance exceeds a predefined level. This construction leads to a random
time to maturity instead of having a fixed exercise day. As shown by Bernard an Cui [7], Timer
options can be priced by solving a partial differential equation or by time-changing the stock
price process and then using Monte-Carlo methods when assuming a diffusion process for the
stock price and the variance. The purpose of this thesis is to show the results of [7] and then
to extend their pricing techniques to jump-diffusion processes for the stock price. The jumps
are assumed to follow a compound Cox process with independent and identically... (More)
Timer options are relatively new exotic options with the feature that they expire as soon as the
accumulated realized variance exceeds a predefined level. This construction leads to a random
time to maturity instead of having a fixed exercise day. As shown by Bernard an Cui [7], Timer
options can be priced by solving a partial differential equation or by time-changing the stock
price process and then using Monte-Carlo methods when assuming a diffusion process for the
stock price and the variance. The purpose of this thesis is to show the results of [7] and then
to extend their pricing techniques to jump-diffusion processes for the stock price. The jumps
are assumed to follow a compound Cox process with independent and identically distributed
jumps. Due to the jumps, the partial differential equation extends to a partial integro-differential
equation. Furthermore, one can time-change the stock price process like in [7] and then use
an adapted Monte-Carlo method with control variates to efficiently simulate the price of a Timer
option. As an example, results for Timer Calls are shown when using Monte-Carlo methods.
Finally, the pricing error for Timer Calls is studied when assuming a stock price process with
continuous paths although it jumps. (Less)
Please use this url to cite or link to this publication:
author
Müller, Janis
supervisor
organization
course
MASM01 20141
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
4390119
date added to LUP
2014-04-04 11:20:43
date last changed
2014-04-04 11:20:43
@misc{4390119,
  abstract     = {Timer options are relatively new exotic options with the feature that they expire as soon as the
accumulated realized variance exceeds a predefined level. This construction leads to a random
time to maturity instead of having a fixed exercise day. As shown by Bernard an Cui [7], Timer
options can be priced by solving a partial differential equation or by time-changing the stock
price process and then using Monte-Carlo methods when assuming a diffusion process for the
stock price and the variance. The purpose of this thesis is to show the results of [7] and then
to extend their pricing techniques to jump-diffusion processes for the stock price. The jumps
are assumed to follow a compound Cox process with independent and identically distributed
jumps. Due to the jumps, the partial differential equation extends to a partial integro-differential
equation. Furthermore, one can time-change the stock price process like in [7] and then use
an adapted Monte-Carlo method with control variates to efficiently simulate the price of a Timer
option. As an example, results for Timer Calls are shown when using Monte-Carlo methods.
Finally, the pricing error for Timer Calls is studied when assuming a stock price process with
continuous paths although it jumps.},
  author       = {Müller, Janis},
  language     = {eng},
  note         = {Student Paper},
  title        = {Pricing Timer Options under Jump-Diffusion Processes},
  year         = {2014},
}