Pricing Timer Options under Jump-Diffusion Processes
(2014) MASM01 20141Mathematical 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:
http://lup.lub.lu.se/student-papers/record/4390119
- author
- Müller, Janis
- supervisor
- organization
- course
- MASM01 20141
- year
- 2014
- 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}}, }