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Ch 05: Assignment - Financial Options Learn Corp. (Ticker: LC), an education technology company, is considered to be one of the least risky companies in the education sector. Investors trade call options for Learn Corp., whose stock is currently trading at $45.00. Suppose you are interested in buying a call option with a strike price of $36.00 that expires in 6 months. (Assume that you get the option for free!) Based on speculations and probability analysis, you compute and collect the following information for your price analysis of the option: For LC's options, time until expiration (t) is taken as 0.50 year (6 months / 12 months). LC's stock could go up by a factor of 2.10 (u). LC's stock could decline by a factor of 0.65 (d). At this time, LC's stock price is out-of-the-money , and if you exercised the option, your payoff would be $36.00. Therefore, if the option is in-the-money, you should exercise the option. Calculate the ending stock price of Learn Corp. for both possible outcomes and the payoff in both situations. Price Increases Stock price P[u) Payoff Cu Price Decreases Stock price P(d) Payoff Co Investors use options and stocks, based on the range in which a stock is likely to go up or go down to create portfolios that help them generate riskless payoffs. This is called creating a hedge portfolio Suppose you sell one call option on Learn Corp.'s stock to create a riskless hedged portfolio. Your hedge portfolio will have a certain number of shares and a certain value based on the payoff it generates. Based on your understanding of a hedge portfolio and assuming 365 day-based compounding, complete the following steps to find the value of the call option Step 1: The total number of shares of LC's stock in the portfolio is (rounded to four decimal places). Step 2: The payoff from the portfolio is (rounded to four decimal places). Step 3: If the annual risk-free rate is 5%, the current value of the portfolio will be Suppose you sell one call option on Learn Corp.'s stock to create a riskless hedged portfolio. Your hedge portfolio will have a certain number of shares and a certain value based on the payoff it generates. Based on your understanding of a hedge portfolio and assuming 365 day-based compounding, complete the following steps to find the value of the call option. Step 1: The total number of shares of LC's stock in the portfolio is rounded to four decimal places). Step 2: The payoff from the portfolio is (rounded to four decimal places). Step 3: If the annual risk-free rate is 5%, the current value of the portfolio will be (rounded to four decimal places). Step 4: The current value of the option is rounded to four decimal places). After you find the value of your option, you discuss it with a friend. She says she will use the information you gave her to replicate the option payoffs. This is called a replicating portfolio Based on your understanding of replicating portfolios, is the following statement true or false