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Option pricing model - Binomial approach Learn Corp. ( Ticker: LC ) , an education technology company, is considered to be one of the least
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 $ Suppose you are interested in buying a call option with a strike price of
$ that expires in 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 year months months
LCs stock could go up by a factor of u
LCs stock could decline by a factor of d
At this time, LCs stock price is
and if you exercised the option, your payoff would be
Therefore, if the option
is outofthemoney, you
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
Payoff
Price Decreases
Stock price
Payoff
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 daybased compounding, complete the following steps to find the value of the call
option.
Step : The total number of shares of LCs stock in the portfolio is
Step : The payoff from the down portfolio i:
Step : If the annual riskfree rate is the current value of the down portfolio will be
Step : The current value of the option is
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?
The cost of the replicating portfolio will be equal to the value of the call option or else arbitrage will drive the prices to be equal.
True
False
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