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. " Option Spreads and Assignment Riske To reduce the risk or capital requirements for an option position, investors and speculators may elect to use option spreads, i.e., a combination of two or more options to express a view. In this exercise, we will consider a bear call spread in which a call option with a lower strike price (K1) is sold for premium c, and an option with a higher strike price (K2) is bought for premium c2. The premium for the call option with the lower strike price is greater than the premium for the call option with the higher strike price, leading to a cash inflow when establishing the position. ~ A Profit Short Call, Strike K1 K1 ST Long Call, Strike K2 Profit from bear spread created using call options. ~ John C. Hull, Options, Futures, and Other Derivatives (Boston: Pearson, 2015).~ Assume the following scenario. You are a wealth manager, and you are selling out-of-the-money bear call spreads on the S&P 500 index (SPX) to generate additional income. Currently, the index is trading at 5,000 points. You decide to sell the 5,250 call which trades at $105 and to buy the 5,350 call which trades at $90.~ The contract size for SPX index options is $100 x index value. Therefore, selling the 5,250 call yields $10,500 in premium and buying the $5,350 call costs $9,000 in premium. Note that SPX index options settle in cash.