Reference no: EM132384636

FB308 Financial Modelling and Coding-Queensland University of Technology- Australia

Project

Background

In this project we will consider some simulation and forecasting problems.

You can use the same data from Project 1 when required here. Not all tasks here require using the data.

Style of your report: Same style as Project 1

Task 1: NPV simulation

A project has an initial cost of $40 and a life of 5 years.

Current annual costs are $100 and will grow at 2.5%p.a. for the next 5 years.

Current annual revenues are $110. Based on historical data, annual revenues are expected to grow according to the following AR model:
rev_t = 15 + 0.9 rev_t-1 + ∈_t , ∈_t ∼ N(0, σ_∈²  = 5)

You are required to simulate revenues to simulate NPVs. Assume a discount rate of 5%p.a.

What is the probability that NPV < 0?

Task 2: Simulation and option pricing

For this task start from the code in simprice single.m.

Assume an initial price S₀ = $30 mean return equal to µ = r_f = 3%p.a. and volatility of returns σ = 25%p.a.

Complete the following:

• Compute the 5^th percentile of simulated prices

• What is the probability that the price in 250 days will be lower than S₀?

• Given an exercise price of X = $35 what is the value of a standard European call option that expires in 250 days (1 year)?

Task 3:

For this task you can start from the code you wrote to simulate prices in Task 2.

You need to change the code to simulate a price series for 250 days where the volatility evolves according to the GARCH process:
σ2_t = 0.000001 + 0.05r ² _t-1 + 0.9σ ² _t-1

starting from the current conditions today of S_T = $10, r_T = 0.002, σ²_T = 0.00025 and assuming a mean return equal to µ = 12%p.a.

Task 4: Comparing forecast accuracy

Within a rolling window framework, compare the accuracy of an EWMA forecast, and forecasts from an AR model with 2 lags and an AR model with 4 lags.

You can use the Rolling fore.m as a starting point, this provides the rolling window code and is discussed in slides 10-13 in the Forecasting Lecture. Forecasting using the AR model is discussed slides 13-15.

Run the analysis on on data for the index and one of your individual stocks. Compare the different models in each case (stock and index) by computing the mean of the squared forecast error for each model.

Task 5: Forecasting portfolio weights

Use the rolling window framework. Take the same three stocks that you used in Project 1. Use the multivariate EWMA smoother to generate 1 day ahead forecasts of the covariance matrix and then compute GMVP weights. Compare the performance of your portfolio (based on forecasting the covariance matrix) against an equally weighted portfolio.

Hints:

• Again start from Rolling fore.m for the rolling window framework

• Refer back to slides 16-18 from the Forecasting lecture

• Need to use the multivariate EWMA smoother to construct the covariance matrix for each estimation window

Attachment:- Final Stock Prices.rar