The (very last) deadline: 23:59 on Sunday 22nd March 2020
Computational Finance
[35 marks:]
Please write a C++ programme that performs the pricing of the following structured note. It is a note
dependent on two interest rates, IR1 and IR2 (that could co
espond to two different points on eg the
GBP curve), and an exchange rate (eg EUR/USD) denoted G. The note pays, at the close of its
maturity day T:
[GT-K]+ . τ/T
where τ.360 is the number of days where, at the close, the difference (in absolute value) between IR1
and IR2 is (strictly) lower than: 25% * min{IR1,IR2}. (We follow the convention ACTUAL/360 for time
measurement.) You may assume that all three stochastic processes follow geometric Brownian
motions. Without loss of generality you may assume that the two IRs have equal initial values.
In addition to providing basic pricing, your programme should facilitate sensitivity analysis.
Please write a report (and please make it as concise and to-the-point as possible, and please make it
use itemising/enumerating whenever possible) that:
[35 marks:]
Part One:
0) Starts by a
ief introduction focusing in particular on any differences/divergences from the in-
class approach; and then
1) Presents a decent illustration of the effect on the price of both:
o The co
elation between the two IR rates; and
o The volatilities of the IR rates
And please comment on the intuition behind your findings.
2) Lists, and
iefly explains, the (top three) value-adding elements (eg in providing extra
sophistication/accuracy) of your code, compared to the in-class programme;
3) Lists, and
iefly explains, the main (say, three) approximations to (or simplifications of)
eality, that you have resorted to;
4) Lists, and
iefly explains, the main (say, three) opportunities for future work that remain.
[30 marks:]
Part Two:
Then please answer the following questions. They touch on the
oad area you have worked on
above. Please give succinct (rather than lengthy) answers.
a) In your coding above, have you identified a shortcut, that provides a great efficiency
compared to a
ute force method? If so, what is it?
) What are the main disadvantages of using geometric Brownian motion to model interest
ates?
c) Can you mention a related note (to the one above) that happens to have the opposite
co
elation profile? (Please give the co
esponding payoff.)
For the remaining questions, please indicate whether True or False. (Importantly, please include a
convincing and targeted explanation of why.)
d) If your implementation of the explicit scheme of finite difference methods is cu
ently stable, it
then follows if you halve your time step (delta_t), your scheme will definitely remain stable.
e) If you double the number of paths (simulations) in your (pseudorandom number) Monte Carlo,
you have halved the likely Monte Carlo e
or (ie you have doubled the accuracy).
f) Let Z1 and Z2 be two independent N(0,1) random variables. It then follows that 2Z1–3Z2 and
3Z1+2Z2 are identically distributed.
(Remember that notation N(a, b) means normal with mean a and variance b.)
NB:
- Please submit both the code (source file) and the report (the latter should preferably be in
Word format) plus any spreadsheet you used. You should also include the code (source file)
from your C++ project as an appendix (preserving the default C++ Editor colours) to your
eport.
- In your report’s answers, please use the same numbering used in the questions above.
- Please make sure that any (academic or other) sources are properly referenced.
- [To be confirmed:] Please note that the Keats submission facility is likely to permit you to
submit only a maximum of three files.
- And finally: Please submit well ahead of the deadline. (Problems that arose for late
submitters in the past include, among many other incidents, discovering that their
login/password had expired. It only took them a few minutes to revive them, but because they
left it so close to the deadline, they ended up missing the cut-off time. There are plenty of
other incidents reported by later submitters – an unexpected loss of internet connection, etc,
etc – so please do not treat the deadline as a target. Rather, it is a cliff edge to stay well clear
of.)
The (very last) deadline: 23:59 on Sunday 22nd March 2020
Financial Engineering
[35 marks:]
Please build a spreadsheet, equipped with a VBA programme, that performs and illustrates the
calculation of the CVA arising from a portfolio (a netting set) consisting of: (A) a forward contract that
is long the underlying, and (B) a forward contract that is short the underlying. The two underlyings are
different, but the two forwards have the same maturity. The notional of (A) should be greater than the
notional of (B). As many of the calculations as possible should be placed in the VBA module(s). In
addition to providing central estimates, your tool should facilitate a prudential-valuation analysis.
Please write a report (and please make it as concise and to-the-point as possible, and please make it
use itemising/enumerating whenever possible) that:
[35 marks:]
Part One:
0) Starts by a
ief introduction focusing in particular on any differences/divergences from the in-
class approach; and then
1) Presents a decent illustration of the exposure profile(s) generated by the tool, and
iefly
comments on the intuition behind them.
2) Lists, and
iefly explains, the (top three) value-adding elements (eg in providing extra
sophistication/accuracy) of your tool, compared to the in-class spreadsheet;
3) Lists, and
iefly explains, the main (say, three) approximations to (or simplifications of)
eality, that you have resorted to;
4) Lists, and
iefly explains, the main (say, three) opportunities for future work that remain.
[30 marks:]
Part Two:
Then please answer the following questions. They touch on the
oad area you have worked on
above. Please give succinct (rather than lengthy) answers.
a) Assume that the discount rate is exactly 0 (and the following monetary values are in $million).
Picking a time horizon, T, you are told that (as calculated at time zero), for a particular
portfolio, the EPE is 3 and the ENE is 9 (both co
esponding to T). Is this enough to deduce
the expected exposure / valuation (again measured at time 0) of that portfolio, co
esponding
to time horizon T? If so, what is it?
) (Without loss of generality assume that the expected/maximal exposures mentioned here
co
espond to a single time point in future, T.) Bank A uses for economic capital (EC) a
measure equal to: 1.4 * EPE. Bank B, instead, uses the weighted average: 80% * EPE + 20%
* ME. How small does the ME (maximal exposure) need to be, relative to the EPE, for Bank A
to end up putting aside (for this specific EC aspect) more EC than Bank B?
c) Write a piece of VBA code, a macro called readAndPrint, that reads the contents of cells A1
to (horizontally) J1 of sheet “readFrom”, and then prints to cell A1 of sheet “printTo” the
individual cell contents (that have been read) separated by commas, with that whole result
enclosed in
ackets.
For example, if the cell content of A1 to J1 of sheet “readFrom” is:
a B 50 6 t XXXXXXXXXX
the macro then prints into A1 of sheet “printTo” the following string: (a,b,50,6,t,5,6,8,8,0)
NB: Please make sure you use an iteration loop when iterating through the input cells (rather
than doing the iterating manually).
For the remaining questions, please indicate whether True or False. (Importantly, please include a
convincing and targeted explanation of why.)
d) If the presumed recovery on a reference entity goes up (and assuming all other market
variables of relevance are unchanged), then the implied default probability goes down.
e) Take two counterparties with identical exposure profiles, but they differ in their credit qualities:
A has a low credit spread, and B has a high credit spread. It then follows that a stress test
that bumps credit spreads up by 100bp will result in a higher CVA increase for A than for B.
f) (Assume the discount rate to be zero in this question). For a stock, that is now worth $100,
and that makes between now and 1 year time two (discrete) dividend payments: $5 (in 1
month time) and $10 (in 9 months time), it then follows that the (continuous-compounding
quoted) dividend yield (up to 1 year) is exactly equal to 15%.
NB:
- Please submit both the spreadsheet and the report (the latter should preferably be in Word
format). You should also include the code from your module(s) as an appendix (preserving
the default VBA Editor colours) to your report.
- In your report’s answers, please use the same numbering used in the questions above.
- Please make sure that any (academic or other) sources are properly referenced.
- [To be confirmed:] Please note that the Keats submission facility is likely to permit you to
submit only a maximum of three files.
- And finally: Please submit well ahead of the deadline. (Problems that arose for late
submitters in the past include, among many other incidents, discovering that their
login/password had expired. It only took them a few minutes to revive them, but because they
left it so close to the deadline, they ended up missing the cut-off time. There are plenty of
other incidents reported by later submitters – an unexpected loss of internet connection, etc,
etc – so please do not treat the deadline as a target. Rather, it is a cliff edge to stay well clear
of.)