PAPER CODE EXAMINER DEPARTMENT TEL MTH319 Yi Hong FM 1729 1st SEMESTER 2020/21 Assignment ONE Financial Engineering SUBMISSION DEADLINE: 5:00 PM on Sunday November 8, 2020 INSTRUCTIONS TO CANDIDATES 1. The assignment comprises 15% weight of the final module mark. 2. Write a report about the performance of hedging strategies (details and guidelines attached). 3. The report must be written in English, associated with the supportive excel files. 4. University policy on late submission will be followed. Introduction This part of the course assessment is worth 15% of the final mark for the course, and consists of a take‐home individual course assignment that will be worked on and submitted individually. This project aims to practice your skills in pricing, hedging and trading involving options, stocks and bonds in the context of Monte Carlo simulations. SCENARIO: Suppose you are working on a security market consisting of a stock, a Treasury bond and a European (call/put) option: 1) a Treasury bond delivers the annual yield of 2.50% (r = 2.5%) with continuous compounding, and has the infinity maturity (TBond=∞). Under a risk‐neutral probability measure Q, the bond price follows a process as follows: ( ) ( ) dB t rdt B t And the current bond price is $1.0, e.g., B(0) =1. 2) the stock price follows a geometric Brownian motion. Under a risk‐neutral probability measure Q, the process for the stock price is given by: ( ) ( ) Q t dS t rdt dW S t And The current stock price is $100, e.g., 0 $100S , and the volatility of this stock is 40% per annum, e.g., 40% . 3) A European option on this stock (or Option A) is specified with the strike price of $100 (e.g., K=$100) and the time‐to‐maturity of 2 years (e.g., TA=2 years). YOU may decide the type of Option A: either call/put. Requirements: I. PART I (Numerical Analysis) (50%) a) Conduct the Monte Carlo simulation and work out the price of this European option with the number of simulation paths equal to M= 5000. (20%) b) Conduct the performance analysis 1) by changing the number of simulation paths (e.g., M=1000, 3000, 5000, 8000, 10000 and etc.) 2) by changing the number of time steps in each simulation path (e.g., N= 500, 1000, 4000, 6000, 8000 and etc.). Plot your numerical results. (15%) c) Estimate the probability functions of strike price at maturity (e.g., TA=2 years) by using the result as follows: 2 0 0 2( ) ; (1 )TrT rTT S K c cprob S K e prob e K K , based on the simulation conducted in a) by setting a range of { }( 0,1,...,50)K K i i . Plot these estimated probabilities. (15%) II. PART II (Trading Strategies) (40%) Suppose that there is another European option (Option B) written on this stock with a different strike K=$110 but with maturity of 3 years (TB= 3 years). YOU may decide the type of Option B: either call/put. Assume now that you have taken a short position in the European option with the quantity of 1 (e.g., nA = ‐1) d) Develop the delta‐neutral strategy to hedge your short position in Option A by using the portfolio of stocks and bonds. Plot 1) the time series of replication errors of your hedging portfolio (involving option A, stocks and bonds) and 2) terminal payoff of Option A against the payoff of the portfolio of stocks and bonds across different stock prices at maturity. (20%) e) Develop the delta‐gamma neutral strategy to hedge your short position in Option A by using the portfolio of stocks, bonds and options B. Plot 1) the time series of replication errors of your hedged portfolio (involving option A, stocks, bonds and option B) and 2) the terminal payoff of Option A against the payoff of the portfolio of stocks, bonds and option B across different stock prices at maturity. (20%) III. PART III (Reporting) (10%) Summary all the results in Part I and Part II and make comments on your results accordingly with the maximum of 600 words. For example, you may report your numerical results by briefly describe the methodology at first, and make comments on your plots in PART I. Also, you may assess the performance and features (i.e., advantages and disadvantages) of the hedging strategies developed in PART II. Assignment Guideline This assignment assesses Learning Outcome A‐D. Note that you need: 1) Show all the results with comprehensive interpretations in a report (with the maximum 15 pages); 2) Show other relevant and supportive results in Python programme code or other program language code. As the outcome from this project, you are expected to submit a report, associated with the code files. Please disclose the detailed process/results as much as possible (e.g., the methodology and implementation of Monte Carlo simulation and the development of delta‐neutral and delta‐gamma‐neutral hedging strategies). The deadline of the assignment submission to ICE is at 5pm on November 8, 2019 (Week 8). Your analysis has to be your own, demonstrating your own ideas and independent and critical thinking (and not those of somebody else). However, your report must include: 1) A brief description of the project In the first section, your work should contain a formal introductory section that provides an overview of the project, including the title of the project, the setup of the securities market and the process of asset prices and the main goals that this project aims to achieve. 2) Process of the optimal hedging strategies and performance analysis After specifying the security market that you are working on, you are ready to complete the tasks in I) and II) which can be presented in two separate sections. It is suggested that you describe the process of Monte Carlo simulation in the market in detail and report the performance analysis of your implementation and the estimated probability plots as well, and then provide the details about the development of the delta‐neutral and delta‐gamma‐ neutral hedging strategies, followed the performance analysis of hedging portfolios. Also, please clearly explain how you obtain the required results, supported by your models in code files. Note: the lecture and tutorial in Week 5&6 will demonstrate the strategy how to complete these tasks in a simplified case. 3) Comments on results In the final section, you need evaluate the implementation process of PART I and II in terms of the pricing and hedging performance in the context of Monte Carlo simulation. It is very important for you to understand those theoretical results discussed in the lectures by conducting practical investigations in a specified market, which will help to improve your skills in financial modelling and investment management in practice. Submission: each of you submits only ONE report and ONE code file. In the first page, please list your name(s) and student ID(s).
欢迎咨询51作业君
