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

ASSIGNMENT 5

FIN 224

Fall 2023

Note: if you are choosing to use your test scores instead of the final exam, you will have to submit this Assignment working individually. Everyone who does not take the final will have to submit Assignment 5 so that I have an assessment of you for the last three weeks of material in the course.

If you and your group mates are all taking the final exam, you may work in a group of up to 4 on this Assignment.  Please indicate clearly on your Assignment who the members of the group are. Please note, all assignments submitted with more than 4 group members will automatically receive a 0 grade. 

This Assignment is due on Wednesday, December 13th at 9:00pm (EST) at the submission link in Blackboard. No late assignments will be accepted.

1. Pick an option on a stock that does not pay a dividend (other those we discussed in class).

(a)  Using May or June 2024 options, calculate the implied volatility of the stock using Rf = .05, t=approximate monthly time remaining, and a strike price close to the stock price.

(b) Calculate the theta each day for the next 30 days assuming all other inputs stay the same (note: this is the change in the option price due to the change in time)

(c) Using each day’s closing price over the last 11 trading days, calculate

(i) the option price each day (using that day’s stock price and implied volatility from (a))

(ii) the delta for each of the last 11 days

(iii) the gamma for the last 10 days (note: this is the change in the delta so you will only have this for ten days)

2. Gold is currently trading for about 2,100 per ounce. You are considering 3 ways of taking a short position on gold: (i) sell 100 ounces of gold short, (ii) take a short position in 1000 gold futures (June 2024), (iii) buy a futures put options on 1000 gold futures at K=2100 (June 2024).

(a)  If you enter the above positions when gold equals 2,100, compare the dollars in profit from the three ways of betting against the price of gold if gold ends up at the following prices at time t: 1850, 1900, 1950, 2000, 2050, 2100, 2150, 2200, 2250, 2300, 2350 (Note: you should assume the price of one futures put option is $10).

(b) Draw a diagram showing the profits for each position for each price of gold.

(c) Which option has the lowest risk? Explain

3. (a) Choose a stock that does not pay a dividend. Find a real-world split-strike strategy (where you sell a call option and use the proceeds to buy a put option). (Note: you should find a call with a price >= the put you buy so it is a zero cost strategy)

(b) Assume you own the stock and the two options from part (a ), create a chart that shows your net position if the stock price has the following changes at time t: -25%, -20%, -15%, -10%, -5%, 0, 5%, 10%, 15%, 20%, 25%

(c) Using a fair estimate for volatility (you can use implied volatility!) and the normal distribution, approximately what percentage of the time do you expect both the call and put options to be worthless at time t? (Note: there are several ways of estimating this that we have talked about throughout the semester)