[35 marks:]
Computational Finance
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 correspond to two different points on eg the EUR curve), and a stock price S. It pays, upon the close of its maturing day T:
[ST-K]+ . ¦Ó/T
where ¦Ó.360 is the number of days where, at the close, the difference (in absolute value) between IR1 and IR2 is (strictly) higher than: 20% * min{IR1,IR2}. You may assume that all three stochastic processes are assumed to 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. Write a report (and please make it as concise and to-the-point as possible) that:
[35 marks:] Part One:
0) Starts by a brief 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 correlation 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 briefly 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 briefly explains, the main (say, three) approximations to (or simplifications of) reality, that you have resorted to;
4) Lists, and briefly 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 broad 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 brute force method? If so, what is it?
Please return by 23 March 2019
b) What are the main disadvantages of using geometric Brownian motion to model interest rates?
c) Can you mention a related note (to the one above) that happens to have the opposite correlation profile? (Please give the corresponding payoff.)
For the remaining questions, please indicate whether True or False. (Importantly, please include a convincing and targeted explanation of why.)
d) The explicit scheme of finite difference methods is unconditionally stable.
e) On a binomial tree, a put option is considerably more difficult to price than a call option.
f) Let Z1 and Z2 be two independent N(0,1) random variables. It then follows that Z1-Z2 and
Z1+Z2 are two N(0,2) random variables with correlation coefficient -1. (Remember that notation N(a, b) means normal with mean a and variance b.)
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.