Consider American call options written on S&P 500 etf (SPY). This etf pays dividends on June...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider American call options written on S&P 500 etf (SPY). This etf pays dividends on June 18th. Therefore, we will use BSM formula to price call options maturing on June 16h. Go to finance.yahoo, copy and paste the table with current prices on these options maturing on June 16th to the excel spreadsheet. Consider 10 call options which differ by their strike prices: 5 options in-the-money and 5 options out-of-the-money. The difference between two adjacent strike prices should be $2. Make a table showing the stock (SPY) price, 10 strike prices and corresponding option prices, where option prices must be equal to the mean between the bid and the ask price. Find the expiration time, T, of the options 2. (10 MARKS) Find the historical standard deviation, o, of SPY returns based on the previous three months. (Use daily prices of SPY from finance.yahoo) 3. (30 MARKS) Assume that the continuously compounded risk-free rate is 0.1%. Use BSM formula to find the prices of the call options with the time to maturity, stock price, and strike prices from Q.1 and a from Q.2. Make a table with the following columns: Stock price, o, Strike Price, di, d2, N(d), N(d2), Price of Call option. The table should have 10 rows corresponding to 10 different strike prices used in Q.1 4. (30 MARKS) Find the implied volatilities for 10 strike prices from Q.1. Make a table showing the moneyness of the option (K/S), price of the option, and the implied volatility. Plot the implied volatility versus moneyness. How do you explain the shape of the curve? How it is related to the standard deviation, o, found in Q.2? At what strike price options are overpriced the most with respect to the BSM price? Part II (not related to part I) (20 MARKS) Assume that the assumptions of BSM model hold. Consider European call option with strike price K-40, T=.25 written on the stock with So=40, µ=0.10, o = 0.25. The risk-free rate r is 1.0%. Find the expected return (under real probabilities) of the call option between today and time to maturity. Repeat this exercise for So=30, 35, 45, and 50. What do you conclude about the expected return of the option versus its moneyness? (Hint: Take into account that the expected payoff, E(Cr), where the expectation is taken under real probabilities, could be found from the result for Eº(CT), where the expectation is taken under risk- neutral probabilities of stock returns. The two probability distributions differ only in their expected values. The expected return under real probabilities is u, while the expected return under risk-neutral probabilities is r) Consider American call options written on S&P 500 etf (SPY). This etf pays dividends on June 18th. Therefore, we will use BSM formula to price call options maturing on June 16h. Go to finance.yahoo, copy and paste the table with current prices on these options maturing on June 16th to the excel spreadsheet. Consider 10 call options which differ by their strike prices: 5 options in-the-money and 5 options out-of-the-money. The difference between two adjacent strike prices should be $2. Make a table showing the stock (SPY) price, 10 strike prices and corresponding option prices, where option prices must be equal to the mean between the bid and the ask price. Find the expiration time, T, of the options 2. (10 MARKS) Find the historical standard deviation, o, of SPY returns based on the previous three months. (Use daily prices of SPY from finance.yahoo) 3. (30 MARKS) Assume that the continuously compounded risk-free rate is 0.1%. Use BSM formula to find the prices of the call options with the time to maturity, stock price, and strike prices from Q.1 and a from Q.2. Make a table with the following columns: Stock price, o, Strike Price, di, d2, N(d), N(d2), Price of Call option. The table should have 10 rows corresponding to 10 different strike prices used in Q.1 4. (30 MARKS) Find the implied volatilities for 10 strike prices from Q.1. Make a table showing the moneyness of the option (K/S), price of the option, and the implied volatility. Plot the implied volatility versus moneyness. How do you explain the shape of the curve? How it is related to the standard deviation, o, found in Q.2? At what strike price options are overpriced the most with respect to the BSM price? Part II (not related to part I) (20 MARKS) Assume that the assumptions of BSM model hold. Consider European call option with strike price K-40, T=.25 written on the stock with So=40, µ=0.10, o = 0.25. The risk-free rate r is 1.0%. Find the expected return (under real probabilities) of the call option between today and time to maturity. Repeat this exercise for So=30, 35, 45, and 50. What do you conclude about the expected return of the option versus its moneyness? (Hint: Take into account that the expected payoff, E(Cr), where the expectation is taken under real probabilities, could be found from the result for Eº(CT), where the expectation is taken under risk- neutral probabilities of stock returns. The two probability distributions differ only in their expected values. The expected return under real probabilities is u, while the expected return under risk-neutral probabilities is r)
Expert Answer:
Answer rating: 100% (QA)
Here are the detailed steps and calculations for each part of the question 1 SPY option prices from Yahoo Finance on 6102022 Strike Price Option Price ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these accounting questions
-
How can we demonstrate that the different dimensions of culture comprise a whole?
-
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
-
Consider Black Scholes model 1. What are the assumptions of BS model? 2. Suppose you are given: (a) S(0) = 100 (b) Stock price S(t) follows the BS model (c) The stock pays continuous dividends at a...
-
In preparing the consolidation worksheet for Bolger Corporation and its 60 percent owned subsidiary, Feldman Company, the following elimination entries were proposed by Bolgers bookkeeper: Bolger's...
-
What is the entry for the down payment from a signed contract?
-
For each of the following items, circle either a or b. In some cases, both a and b may apply to you. You should decide which is more like you, even if it is only slightly more true. On a project, I...
-
Using the provided code for performing Gibbs sampling for binary GP classification, compute the \(\hat{R}\) value for one of the training latent function values. How many samples need to be drawn...
-
Indicate the effectUnderstate, Overstate, No Effectthat each of the following errors has on 2010 net income and 2011 net income. 2010 2011 (a) Equipment purchased in 2009 was expensed. _____ _____...
-
Q5. (Ch 11) At the close of Friday (Nov 13th), NIO is trading at $44. If you look at the call options that expires next Friday (Nov 15th) with a strike price of $45, $48, and $50, their prices are...
-
Regulators, in protecting the public interest, are examining Wincox Insurance Company's financial statements. These regulators impose requirements on Wincox's financial statements because of which...
-
Should a country attempt to achieve IRP? What policy options the government has achieve IRP? Explain the steps in testing IRP with real data. With the growth of big data and the use of technology in...
-
What are the major technological trends materially influencing the provision of financial services? How is the competitive landscape shaping adoption of these new technologies around the globe? How...
-
per yr III. Asset historical cost is $ 25,500. Salvage is 5,000. Useful life is 3 years. Asset was purchased on January 1, 2023. Using the Double Declining Balance method, calculate the following:...
-
a) With the aid of an appropriate diagram, show the relation between shear stress and the velocity gradient du/dx for: i) water; [2 marks] ii) non-drip paints (shear thickening). [2 marks] b)...
-
E8.2 Compute the theoretical ACF of the following processes: (i) v[k] e[k] + 0.8e[k - 1] + 0.15e[k - 2] (ii) v[k] = 0.95v[k 1] + e[k] (iii) v[k] = 0.4v[k 1] + e[k] +0.6e[k - 2] (iv) v[k] = -0.7v[k -...
-
On January 1, 2023, Flounder Corporation, a public company following IFRS, acquired 17,400 of the 58,000 outstanding common shares of Noah Corp. for $27 per share. Noah's statement of financial...
-
Data table Time Harris Pinwheel 1 2 3 $9 $20 10 32 12 28 4 17 25 (Click on the icon in order to copy its contents into a spreadsheet.)
-
Will the prediction interval always be wider than the estimation interval for the same value of the independent variable? Briefly explain.
-
Charlie's Green Lawn Care is a cash basis taxpayer. Charlie Adame, the sole proprietor, is considering delaying some of his December 2012 customer billings for lawn care into the next year. In...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family. Ivan and Irene have the following investment income, in addition to that reported in Chapter 1: Dividends...
-
In 2012, Margaret and John Murphy are married taxpayers who file a joint tax return with AGl of $25,000. During the year they incurred the following expenses: Hospitalization insurance...
-
Balance sheet hedging Gateaux Antoinette, SA, a subsidiary of Antoinette Cakes Inc., New York, had cash of 100,000 and accounts receivable of 100,000 each on its books (or 200,000 in total) when the...
-
The equilibrium exchange rate Consider the following quantity of dollars demanded and supplied daily in millions as a function of the dollars peso price, S: a. Solve for the equilibrium exchange rate...
-
Intervention in the foreign exchange market Argentina pegged its currency, the peso, to the US dollar at a rate of 1 to 1 from April 1991 to November 2001. Under the rules of the currency board, the...
Study smarter with the SolutionInn App