代写programming、c/c++编程代做、代写Java，Python语言

日期：2020-04-05 11:26

1. Initialise the random number generator of your chosen programming package using a

2. Generate a price time series using the equation

p(t) = p0(1+A? sin(ωt +0.5η(t)))

where t ranges from 0 to 1 in 1000 time steps, p0 = 100, A = 0.1, and ω = 100. η(t) is a

sequence of i.i.d Gaussian random variables with zero mean and unit variance.

3. Define 3 self-financing long-only trading strategies with initial cash C0 = 1000. The self-

financing condition for the update of cash and volume at each time step is given by

TV(t) = C(t) + p(t)V(t) = C(t +1) + p(t)V(t +1),

for all time steps t. The long-only condition is given by V(t) ≥ 0 for all time steps. No

borrowing is also considered, C(t) ≥ 0 for all time steps.

4. Define the return of a trading strategy a at time t as,

5. Compute 3 representative performance indicators, Sharpe ratio and two alternatives introduced

during lectures, to evaluate the trading strategies. If appropriate, for each of them

provide two independent measures: within a training set and within a test set, representing

70% and 30% of the data, respectively.

6. For the hypotheses that the strategies have a non-zero Sharpe ratio, use a statistical test

covered in the lectures to control for Family Wise Error Rate (FWER) at a confidence

level of 5%. Create another price series of the same size using the same data generating

process and re-evaluate the Sharpe ratio of the strategies. Did the procedure help in

reducing type 1 errors?

7. Summarise and present results with plots and tables.

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Standard and non-standard calculators are permitted

Tasks

Written report A single written report in pdf (maximum 10 pages, code included) structured

into:

? Introduction

? Methodology

? Results

? Discussion

? Bibliography

? Appendix (including code)

Marking The marking will be based on the following criteria:

? Clarity of presentation and explanations;

? Justification of the methodology;

? Critical interpretation of results.

? Consistency of language and mathematical notation;

? Validity of results;