Question
Option pricing model - Binomial approach Learn Corp. (Ticker: LC), an education technology company, is considered to be one of the least risky companies in
Option pricing model - Binomial approach
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 $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 free!) Based on speculations and probability analysis, you compute and collect the following information for your price analysis of the option:
For LCs options, time until expiration (t) is taken as 0.50 year (6 months/12 months). | |
LCs stock could go up by a factor of 1.50 (u). | |
LCs stock could decline by a factor of 0.60 (d). |
At this time, LCs stock price is out-of-the-money , and if you exercised the option, your payoff would be-$7.20 . Therefore, if the option is out-of-the-money, you should not exercise the option.
Calculate the ending stock price of Learn Corp. for both possible outcomes and the payoff in both situations.
Price Increases | Price Decreases | ||
---|---|---|---|
Stock price P(u) | $27.00 | Stock price P(d) | $10.80 |
Payoff Cuu | $1.80 | Payoff Cdd | $0.00 |
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 LCs stock in the portfolio is ________(rounded to four decimal places).
Step 2: The payoff from the portfolio if the stock is down is______ (rounded to four decimal places).
Step 3: If the annual risk-free rate is 6%, the current value of the portfolio if the stock is down will be_______ (rounded to four decimal places).
Step 4: The current value of the option if the stock is down 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.
According to your understanding, your friend will______(buy,sell) the same number of shares of Learn Corp.s stock. She will then borrow an amount equal to the present value of the hedge portfolios payoff at 6%.
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