Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Option pricing

Recall what you have done for your first assignment. Your team leader gave you 9 stocks and asked you to build a portfolio. After you constructed your portfolio and explained him your thoughts, he decided to use the capital elsewhere for the time being and probably invest in your portfolio later in 3 months. (i.e., you didn’t actually implement any buying or selling. What you have is merely the calculation on your computer)

Meanwhile,you realize that JP Morgan already possesses some stocks in its asset pool, such as Amazon and Tesla. You will probably need to sell them later if your team leader asks you to build your portfolio. However, as the stock prices fluctuate everyday, you are thinking of using an option to hedge the risk, in case you truly need to sell the stocks in 3 months. In order to have more flexibility, you want to be able to exercise that option at any time during that 3-month time period.

Now use your knowledge in option pricing to decide the fair values of such option for Amazon and Tesla stock, respectively :

•  Suppose you are on Oct 27, 2023. (at the time when the stock market  is just about to be closed) The risk-free rate of return is still 2.07% p.a.

•  You want to acquire the options that are “at-the-money” .

•  You can reuse the historical prices you retrieved last time to calculate other parameters you need.

•   Build your own binomial tree and apply the technique learned in the exercise class. The number of periods N = 20.

•   Double-check your results by applying crrtree in Financial Instruments Toolbox

•   Revisit the dashboard you built via App Designer in your firstassignment. Add the option values of the 2 stocks in that table you created last time. (you are expected to hand in the codes that can  reproduce the entire dashboard with the new information)

Empirical economics

Your team leader also wants you to evaluate the performance of your candidate stocks vs. certain market indices. You can apply the classic CAPM methodology   and estimate the parameters that are necessary for your evaluation.

Consider SP500 index as the market portfolio. (You can reuse the dataset in the exercise)

Since you got only 3-year closing prices in your last assignment, there’s a technique you can apply to get enough samples for your evaluation:

•   Suppose P1, P2, P3, …, Pn,  Pn+1, … are the daily prices on day 1, 2, 3, …, n,   n+1, … in your dataset (in chronological order), you can calculate annual returns by:

(Pn-P1 )/P1,

(Pn+1-P2 )/P2,

(Pn+2 – P3 )/P3

….

These are so-called “daily annual returns”.

•   Create enough such samples (100 at least) to carryout your analysis

•   You only need to analyze the relationship between Google and market index

•   Once you accomplish the calculations / analysis, please interpret your results.