1. The following information about options on Tesla stock is provided: S=200, t =T-t=1 month, r...

 

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1. The following information about options on Tesla stock is provided: S=200, t =T-t=1 month, r = 5% per annum (C.C.), and o = 35% per year, and consider the following options portfolio: Number of contracts (minus sign indicates option written) Strike price Calls Puts 190 200 210 200 210 -2000 -210 -150 0 a) Find the net delta, gamma, and vega exposures of this portfolio? b) How many shares must be sold/purchased to achieve a delta-neutral position? What is the market value of those shares? c) What will happen to the value of the options portfolio if the stock price immediately increases to 250? What is the net gain/loss on the delta-hedged position? d) Now suppose that the portfolio owner decides to make the portfolio both delta and gamma neutral by selling/buying shares and modifying the number of 210-strike price call options in the portfolio. How many of these calls should be bought or sold to achieve a gamma- neutral position? What is the new value for the number of shares that should be bought or sold for delta-neutrality? e) What will be the change in the value of the portfolio in (d) if the stock price increases immediately from 200 to 205? Compare this change to your answer in (c) for the portfolio that was only delta-hedged. Briefly comment. f) Repeat (e) for a stock price decrease from 200 to 195. 1. The following information about options on Tesla stock is provided: S=200, t =T-t=1 month, r = 5% per annum (C.C.), and o = 35% per year, and consider the following options portfolio: Number of contracts (minus sign indicates option written) Strike price Calls Puts 190 200 210 200 210 -2000 -210 -150 0 a) Find the net delta, gamma, and vega exposures of this portfolio? b) How many shares must be sold/purchased to achieve a delta-neutral position? What is the market value of those shares? c) What will happen to the value of the options portfolio if the stock price immediately increases to 250? What is the net gain/loss on the delta-hedged position? d) Now suppose that the portfolio owner decides to make the portfolio both delta and gamma neutral by selling/buying shares and modifying the number of 210-strike price call options in the portfolio. How many of these calls should be bought or sold to achieve a gamma- neutral position? What is the new value for the number of shares that should be bought or sold for delta-neutrality? e) What will be the change in the value of the portfolio in (d) if the stock price increases immediately from 200 to 205? Compare this change to your answer in (c) for the portfolio that was only delta-hedged. Briefly comment. f) Repeat (e) for a stock price decrease from 200 to 195.

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To solve the given questions we need to calculate the net delta gamma and vega exposures of the portfolio and then perform the necessary calculations based on the given information Lets go step by ste... View the full answer