SIMULATION
Assume the stock price S paying a continuous dividend yield q follows the process below
dSt = (r−q)Stdt+σ(St,t)StdWt, (1)
where r is the risk free interest rate and W is a Wiener process under the risk-neutral
probability measure. The local volatility surface has been calibrated with the form. below:
σ(S,t) = 0.25e−t(100/S)α.
We know that the price of an option, V(S,t), on the above stock satisfies the PDE below:
In this project you are asked to price some very popular weakly path dependent option,
such as a Barrier option using both Finite Difference and Monte Carlo Methods.
Barrier options (also called knock-in or knock-out options) are standard calls or puts except
that they disappear (knock-out) or come into existence (knock-in) if the underlying asset
price is found to have crossed a predetermined (barrier) level, B, anytime before the matu-
rity of the option. They have a fairly standard naming convention which describes whether
the barrier is below or above the current asset price (“down” or “up”), whether the option
disappears or appears when the barrier is crossed (“out” or “in”) and whether they have a
standard call or put pay-off. For instance, an up-and-out call option with zero rebate will
have a payoff
hup-and-out call(ST) =
braceleftBigg max(S
T −K,0), if max0≤t≤T St 5
where m is the maximum mark that can be awarded for this assignment, and where d is
the number of days or part days that the assignment is late, i.e. according to the standard
university rules for late submission of assessed work. It is advisable to allow enough time
(at least one hour) to upload your files to avoid possible congestion in Moodle before the
deadline. In the unlikely event of technical problems in Moodle please email your .zip files
to before the deadline.
It may prove impossible to examine projects that cannot be unzipped and opened, and run
on computer lab machines directly from the directories created by unzipping the submitted
.zip files. In such cases a mark of 0 will be recorded. It is therefore essential that all project
files and the directory structure are tested thoroughly on computer lab machines before
being submitted in Moodle. It is advisable to run all such tests starting from the .zip files
about to be submitted, and using a different lab computer to that on which the files have
been created.
A common error is to place some files on a network drive rather than in the submitted
directory. Please bear in mind that testing on a lab computer may not catch the error if the
machine has access to the network drive. However, the markers would have no access to
the file (since they have no access to your part of the network drive) and would be unable
to compile the project. All files must be submitted inside the zipped project directory, and
connected to the project. Please check before submitting