Today is February 1, 2022, and Tesla Inc.s stock is trading for $926.25 in the spot market, off from its ATH of $1,229.91 reached on November 24, 2021, when Elon Musks tax-related selling started bearing down on the stock. Needless to say, it has been quite a ride, both for Tesla fans and for the equity portfolio managers with significant exposure to the meme stock. The table below displays the price of American call and put options on TSLA expiring on April 14, 2022. The risk-free interest rate for this tenor is equal to 8 basis points per year, using the Actual/360 convention. Tesla Inc. does not pay dividends. Feel free to use Prof. John Hulls DerivaGem MS Excel Add-in for this question.

Type Strike price Price

Call 875 127.90

Call 900 116.50

Call 925 102.10

Put 875 73.25

Put 900 84.90

Put 925 100.16

(A) Calculate the implied volatility for each option and describe the pattern that you observe. Is this pattern surprising to you? Does it contravene the law of one price in the option market? Please, discuss briefly.

(B) Calculate the delta, gamma, vega, theta, and rho of each option. Present your results in a neat table displaying each Greek in a separate column.

(C) Assume that you are short 10 contracts of each call option and long 10 contracts of each put option, and calculate the Greeks of your portfolio.