In this practitioner's case study, you will work on two problems revolving around the implementation and risk-profiles of a number of option strategies. 1. Margin Requirements of Naked Options 2. Option Spreads and Assignment Risk Margin Requirement of Naked Options An investor has a margin account with $50,000 in equity, i.e., their own assets, to pursue an option writing strategy. Following FINRA rules, their broker offers them to sell naked options of individual stocks, e.g., options that are not backed by a position in the underlying. 1. For a short call option, the broker demands the greater of (a) Call Price + (20% of the Underlying Price - Out of the Money Amount) or (b) Call Price + (10% of the Underlying Price). 2. For a short put option, the broker demands the greater of (a) Put Price + (20% of the Il;lqdc)rlying Price - Out of the Money Amount) or (b) Put Price + (10% of the Strike rice). Mote that the formula for (a) changes for index options, reducing the requirement to 15% from 20%. The initial margin is the same as the maintenance margin. [f at any point, the margin requirement exceeds the investor's margin buying power, a margin call is issued. The investor believes that the stock of XYZ Corp, currently trading at $50, is unlikely to drop below $45 over the next year and explores the following options with twelve months until expiration to express their view: s Put with a strike price of $50 currently trading at $11. o Put with a strike price of $45, currently trading at $8.40. * Put with a sirike price of $40, currently trading at $6. 'With the information given, answer the following questions. a. Compute the margin requirement per option and calculate how many option contracts for 100 options each the investor can sell for each of the three strike prices. (Remember that the investor receives cash for the option, which needs to be added to their $50,000 equity pile.) b. Assurming the investor chooses to fully exhaust their margin to write these contracts, what is their maximum gain and loss on each position, per option contract and in total? c. Assumne that some time passes, and the stock does not really do much. Then, in one day, the stock price drops to $48. The new prices per option are $10.60 for the $50 put, $7.80 for the $45 put and $5.40 for the $40 put. Compute whether this change would lead to a margin call for any of the three options. d. Let's say that the option seller chooses to \"buy to close their options they have written, i.e., buy them back at the prices in . Compute their return on equity