Question

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 Leam Corp., whose stock is currently trading at $50.00. Suppose you are interested in buying a call option with a strike price of $40.00 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 (1) is taken as 0.50 year (6 months/12 months). • LC's stock could go up by a factor of 1.80 (u). • LC's stock could dedine by a factor of 0.90 (d). the option, your payoff would be $10.00 . Therefore, if the option At this time, LC's stock price is is in the money, you should in the money exercise the option es and the payoff in both situations. Calculate the ending stock price of Learn Corp. for both possible ou Price Increases Stock price P(u) Payoff Co Price Decreases Stock price P(d) Payoff Cd onerata 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 o e Mind Top - Cangas

Answer 1

Upward price for stock	=	50 * 1.8	=	90
Downward price for stock	=	50 * 0.9	=	45
Probability for upward for stock	=	(90 - 50) / (90 - 40)	=	0.8
Therefor probability for downward prices for stock	=		=	0.2
Stock price after 1 year	=	90*0.8 + 45*0.2	=	81
So Stock price after 6 months	=	(81-50)/2 + 50	=	65.5

Now we buy the call with strike price of $ 40. So we would exercise the only when the stock price at the end of 6 months would be above $ 40.

So in this scenario, the premium for call is $ 10 (50-40)

If price increases to 90 & call buy at 40 with premium of $ 10 the net gain would be $ 40.

If price increases to 70 & call buy at 40 with premium of $ 10 the net gain would be $ 20.

If price decreases to 40 & call buy at 40 with premium of $ 10 the net loss would be $ 10.

If price decreases to 45 & call buy at 40 with premium of $ 10 the net loss would be $ 5.

So it would be beneficial to buy the Call as there are high chances for rising in prices of stock.