Compute implied volatility using the black-scholes model

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Reference no: EM132139671

Hedging Assignment -

Your portfolio: A stock is currently trading at 55. You hold a portfolio of the following instruments:

Long 200 shares of stock
Long 200 puts with a strike of 50 and maturity of three months (T=13/52)
Short 200 calls with a strike of 60 and maturity of three months (T=13/52)

All of the options are European options and each option is on 1 share.

This portfolio information and information on interest rate and dividend are contained in the attached Excel file (rows 1-4).

Prices of various options (including the ones held in your portfolio) are listed in the Excel file (see rows 6-12).

Requirements:

a. Based on the option prices, compute their implied volatility using the Black-Scholes model. Record your answers (in Sheet1) in range D7:D12.

b. Based on the computed volatilities and information provided, compute delta, gamma and vega of the 6 options. Record your answers in range E7:G12.

c. What is the objective of the strategy employed in your portfolio? Write the answer (A, B, C or D) in cell B14.

A. Income

B. Insurance

C. Long volatility

D. Short volatility

d. Compute the portfolio's value and write the answer in cell B15.

e. Compute the portfolio's delta and write the answer in cell B16.

f. Compute the portfolio's gamma and write the answer in cell B17.

g. Compute the portfolio's vega and write the answer in cell B18. Note: you may see an alternate formula that expresses vega as option price change for 1 percentage point increase in volatility. Do not use that formula, use the one in the lecture note instead.

For the following parts, treat them as independent from one another, unless stated otherwise. That is, all of them pertain to the original portfolio at the original prices.

h. Use delta and gamma to approximate the portfolio's value if the stock price suddenly increases by $3. Write the answer in cell B19.

i. What is the additional share position in order to make the portfolio delta neutral? E.g. -10 means short 10 shares, +15 means long 15 shares. Write the answer in cell B20.

j. What are the positions in the stock and 55-strike call in order to make the portfolio both delta and gamma neutral? Write the answers in cells B22 and B23 respectively.

k. What is the net cash flow of achieving delta and gamma neutrality for the portfolio using the strategy in (j)? Write the answer in cell B24.

l. What are the positions in the stock and 55-strike put in order to make the portfolio both delta and gamma neutral? Write the answers in cells B26 and B27 respectively.

m. What is the net cash flow of achieving delta and gamma neutrality for the portfolio using the strategy in (l)? Write the answer in cell B28.

n. Compute the delta of a bull spread using calls with strikes of 55 and 60. Assume the strategy is on one unit of shares. Write the answer in cell B29.

o. Compute the gamma of a butterfly spread using calls with strikes of 50, 55 and 60. Assume the strategy is on one unit of shares. Write the answer in cell B30.

Attachment:- Assignment File.rar

Reference no: EM132139671

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Reviews

len2139671

10/13/2018 3:27:49 AM

This is an individual assessment. Each student receives their individualised assignment in the form of a uniquely generated Excel file with one single worksheet “Sheet1”. Record your answersin the same worksheet. The assignment will be auto-marked so you must record your answers in the designated cells of the worksheet. Failure to comply with this requirement may result in your answers not being picked up meaning a zero mark. Direct all queries to Hedging Assignment Forum in Moodle. Marked to total of 10, which accounts for 10% of overall assessment for the unit. To submit your assignment, go to the unit’s site in Moodle, click on “Hedging Assignment” under “Assessments and Exams” and follow the instruction to upload your Excel file (and nothing else). Do not change the name of the Excel file.

len2139671

10/13/2018 3:27:43 AM

Make sure your answer is worksheet “Sheet1” in the file. Do not use this worksheet for anything else apart from recording the answer. Do not insert rows or columns in this worksheet. If you want to perform calculations, use other worksheets. Make sure your answers to calculation questions are numeric, not text. Put-call parity suggests the implied volatilities for a European call and a European put on the same asset, with the same maturity and the strike price, should be the same. Since the option prices provided are expressed with only 2 decimal points, you may get slightly different implied volatilities for the call and the put. Such difference is EXPECTED.

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