3. Option pricing model - Binomial approach Leam 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 $18,00. Suppose you are interested in buying a call option with a strike price of $25.20 that expires in 6 months. (Assume that you get the option for freel) Based on speculations and probability analysis, you compute and collect the foliowing information for your price analysis of the option: - For LCis options, time until expiration (t) is taken as 0.50 year ( 6 months/12 months). - LCis stock could go up by a factor of 1.50(u). - LC's stock could decine by a factor of 0.60(d). Calculate the ending stock price of Learn Corp. for both possible outcomes and the payoff in both situations. Investors use options and stocks, based on the fange in which a stock is likely to go up or go down, to create portfolios that help them generate rivkless payoffs. This is called creating a hedge portfollo. Suppose you sell one call option on Leam Corph's stock to create a riskless hedged pertfolie. Your hedge portfolio wil have a certain number of shares and a certain value based on the payoff it generates: Eased on your understanding of a hedge portfolio and assuming 365 day-based compounding, complete the follawing steps to find the vahe of the call noticf. Step 1i The total number of shares of LCS stock in the portfolio is Step 2: The payoff from the down portfolio is step 3: If the annual risk-free rate is 65 , the current value of the down portfolio wis be Step 4: The currem value of the cption is After you find the value of your eption, you discuss it with a friend. She says she will use the information you gave her to repticate the optien payofr. This is called a replicating portfonio, Hased on your understand of of replcating portfollos, is the following statement true or false? 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 portfollo. Based on your understanding of replicating portfollos, is the following statement true or false? The cost of the replicating portfolio will be equal to the value of the call option or eise arbitrage will drive the prices to be equal. False True 3. Option pricing model - Binomial approach Leam 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 $18,00. Suppose you are interested in buying a call option with a strike price of $25.20 that expires in 6 months. (Assume that you get the option for freel) Based on speculations and probability analysis, you compute and collect the foliowing information for your price analysis of the option: - For LCis options, time until expiration (t) is taken as 0.50 year ( 6 months/12 months). - LCis stock could go up by a factor of 1.50(u). - LC's stock could decine by a factor of 0.60(d). Calculate the ending stock price of Learn Corp. for both possible outcomes and the payoff in both situations. Investors use options and stocks, based on the fange in which a stock is likely to go up or go down, to create portfolios that help them generate rivkless payoffs. This is called creating a hedge portfollo. Suppose you sell one call option on Leam Corph's stock to create a riskless hedged pertfolie. Your hedge portfolio wil have a certain number of shares and a certain value based on the payoff it generates: Eased on your understanding of a hedge portfolio and assuming 365 day-based compounding, complete the follawing steps to find the vahe of the call noticf. Step 1i The total number of shares of LCS stock in the portfolio is Step 2: The payoff from the down portfolio is step 3: If the annual risk-free rate is 65 , the current value of the down portfolio wis be Step 4: The currem value of the cption is After you find the value of your eption, you discuss it with a friend. She says she will use the information you gave her to repticate the optien payofr. This is called a replicating portfonio, Hased on your understand of of replcating portfollos, is the following statement true or false? 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 portfollo. Based on your understanding of replicating portfollos, is the following statement true or false? The cost of the replicating portfolio will be equal to the value of the call option or eise arbitrage will drive the prices to be equal. False True