Assignment

125.350 – Semester 1 – 2025

The EXCEL file (sheet: “option data”) shows the prices of calls and puts at different strike prices of options on Alphabet Inc. (GOOG) on 14th March 2019. The expiration of all options is the same - September 20, 2019.  The market price of the GOOG stock on 14th March 2019 is $1,185.55. You are considering different situations in the market. Answer the following questions in detail (Remember to make buy or sell decisions of the options based on bid/ask prices, not the last prices).

Question 1(a):

Stock prices can go up to $1,240 or more or down to $1,125 or less, but you are unsure about the direction. Identify at least two option strategies that you consider helpful in such a situation. Consider the following three strike prices $1,125, $1,220, and $1,240 when answering the question. Identify how the strike prices for each relevant strategy as well. (marks: 10)

Answer 1(a):

Question 1(b):

At what prices will both strategies make a profit? Show you calculations in detail. (marks: 10)

Answer 1(b):

Question 1(c):

Calculate the outcomes of both strategies if the GOOG stock on September 20, 2019, turned out to be $1,400 or $1,000.  Which strategy do you feel better?   (marks: 10+5)

Answer 1(c):

Question 2(a):

If you expect the stock price to be around $1,100 and it will not move that much, what strategy would you follow to maximize the profit if you consider the following three strike prices: $1,050, $1,100, and $1,150? Detail the strategy with different strike prices.   (marks: 5)

Answer 2(a):

Question 2(b):

Find the maximum profit for such a strategy. Show your calculation. (marks: 10)

Answer 2(b):

Question 2(c):

Find the ranges of prices for which you will have a profit. (marks: 10)

Answer 2(c):

Question 3(a):

In the EXCEL file (sheet: “price data”), you will find the prices of GOOG from March 15, 2019, to September 19, 2019. Calculate the log return and volatility of log returns. Convert daily volatility into yearly volatility by multiplying daily volatility with . Explain how you did it. Report the standard deviation in two digits after decimal. (marks: 10)

Answer 3(a):

Question 3(b):

Given that the market price of the GOOG stock on 15th March 2019 is $1,185.55, calculate the European call price for a strike price of $1,220 using the two-step binomial pricing model. Use the yearly volatility calculated in part 3(a) and the risk-free rate of 1% per annum. Also, you consider the number of days between 14th March 2019 and 20th September 2019 (expiration date) to be 190, and the number of days in a year 365. Show the steps in detail. (marks: 20)

Answer 3(b):

Question 3(c):

Could this be an American option? If so, what would be the American call price?  (marks: 5)

Answer 3(c):

Question 3(d):

Explain why or why not the call price calculated using the binomial model is the same as what you see in the quotations. (marks: 5)     

Answer 3(d):