Pricing Timer Options under JumpDiffusion 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 timechanging the stock
price process and then using MonteCarlo 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 jumpdiffusion 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 timechanging the stock
price process and then using MonteCarlo 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 jumpdiffusion 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 integrodifferential
equation. Furthermore, one can timechange the stock price process like in [7] and then use
an adapted MonteCarlo method with control variates to efficiently simulate the price of a Timer
option. As an example, results for Timer Calls are shown when using MonteCarlo 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/studentpapers/record/4390119
 author
 Müller, Janis
 supervisor

 Magnus Wiktorsson ^{LU}
 organization
 course
 MASM01 20141
 year
 2014
 type
 H2  Master's Degree (Two Years)
 subject
 language
 English
 id
 4390119
 date added to LUP
 20140404 11:20:43
 date last changed
 20140404 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 timechanging the stock price process and then using MonteCarlo 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 jumpdiffusion 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 integrodifferential equation. Furthermore, one can timechange the stock price process like in [7] and then use an adapted MonteCarlo method with control variates to efficiently simulate the price of a Timer option. As an example, results for Timer Calls are shown when using MonteCarlo 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 JumpDiffusion Processes}, year = {2014}, }