Assignment
Question I
A call option contract on Apple Inc's stock gives the buyer of the call the right to purchase 100 shares of Apple's stock for the strike price of $150. This call option is traded on an exchange. How the exchange will adjust the strike price and the number of shares of stocks that one call option contract entitles the buyer of the call to buy if
1) Apple Inc pays 10% stock dividend
2) Apple Inc makes an secondary offering of its stock. This secondary offering increases the total number of shares by 15%
Question II
Assume today is Dec 10, 2020. Options on the stock of Pfizer Inc are on a March cycle. The current stock price of Pfizer Inc is $42/share. An American call on Pfizer Inc's stock with strike price of $50 is available for $2.3. The American call will expire in 7 months. Assume each call gives the buyer of the call the right to purchase 100 shares of stocks.
1) With what expiration months are options on Pfizer Inc's stock are traded now?
2) An investor wants to buy 10 of this American call for cash. What is the margin requirement for his purchase?
3) An investor wants to write 10 of this American call. What is the margin requirement for his sale of the American call?
Question III
The stock price of Alphabet Inc is $1800/share. Assume European options are available on the stock of Alphabet Inc. An European call expiring in 3 months with strike price of $1700 is available for $170 and An European put with the same strike price and same expiration date is also available for $60.
1) How can you construct a straddle with the above European call and European put?
2) What is the profit function of this straddle on the expiration date and draw a diagram of this profit function against the stock price on the expiration date?
3) For what range of stock price, the straddle will lead to a loss on the expiration date?
Questions IV
Assume today is Dec 1, 2020. The stock price of Delta Airline is $42/share. The American call expiring in 6 months with strike price of $50 sells for $3.80. The Delta Airline is not expected to pay any dividend in the next year. The risk free-interest rate is 2% with continuous compounding.
1) What is the put-call parity relation for American options on non-dividend-paying stock?
2) What is the upper and lower bounds of the American put on Delta Airline's stock with the same strike price and expiration date, using the put-call parity relation in part (1)?
Question V
European options (calls and puts) on a non-dividend-paying stock are available with strike prices of $100, $110, $120. The current price of the underlying stock is $110. The price for the calls are $18 and $9 and $3. All those European options (calls and puts) will expire in 6 months. The risk-free interest rate is 3% per annum with continuous compounding.
1) How can you create a butterfly spread with the European calls? Calculate the profit function of the butterfly strategy on the expiration date.
2) Compute the prices of the European puts on the same stock with same strike prices and same expiration dates, rounding the prices to 2 decimals.
3) How can you construct another butterfly spread with the European puts and compute the profit function of this second butterfly spread on the expiration date.
4) Are the profit functions of those two butterfly spreads same?
Question VI
Suppose that today the stock price of the Tesla Inc is $600/share and that the volatility of the stock price is 70% per annum. Tesla Inc is not expected to pay any dividend in the next few years. The risk-free interest rate is 2% per annum with continuous compounding. European call and put options on Tesla Inc‘s stock with strike price $700 are available. The European call and put options will both expire in 6 months.
Answer questions regarding to a two-step binomial model with 3-month time step.
• What is the percentage up movement of the stock price in the binomial model?
• What is the percentage down movement of the stock price in the binomial model?
• What is the probability of an up movement of the stock price in the binomial model in a risk- neutral world?
• Use this two-step binomial model to compute the price of the European call?
• Use this two-step binomial model to compute the price of the European put?
• Suppose an investor writes 10,000 European puts today, assuming each put gives the buyer of the put the right to sell one share of the stock.
1) How many shares of Tesla Inc's stock the investor has to long (or short) to hedge his short position in the European put for the first 3-month period?
2) If at the end of first 3-month period the stock price goes up, how many shares of Tesla Inc's stock the investor has to long(or short) to hedge his short position in the European put for the second 3-month period?
3) If at the end of first 3-month period the stock price goes down, how many shares of Tesla Inc's stock the investor has to long(or short) to hedge his short position for the second 3-month period ?
Question VII
Assume that the stock price St follows geometric Brownian motion. This means we have constants u and σ such that dSt = uStdt + σStdWt where Wt is the standard Brownian motion. Now find the differential form of ln (St). Namely, what is d ln (St)?
Question VIII
The price of Exxon Mobil's stock is $42/share. Exxon Mobil is expected to pay the dividend of $1.00/share in two months and $1.20/share in five months. The volatility of the stock price is 40% per annum. There are European options on the Exxon Mobil's stock available for trading. The strike price of the European options is $50. The European options will expire in 6 months. The risk-free interest rate is 2% per annum with continuous compounding. Answer questions regarding to using Black-Sholes-Merton formulas to compute European options prices. Round all calculation to 4 decimals.
1) What is present value of the dividend payment?
2) What is the price of the European call option, using Black-Sholes-Merton formula?
3) What is the price of European put option, using Black-Sholes-Merton formula?
4) Verify whether the put-call parity of options on stock paying dividend holds?
Format your assignment according to the following formatting requirements:
(1) The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
(2) The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
(3) Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.