# A question on Options - assistance required

Can Some one help with this? Consider a two-period binomial in which a stock currently trades at a price of \$65. The stock price can go up 20% or down 17% each period. The risk free rate is 5%. The price of a call option expiring in two periods, with an exercise price of \$60 is correctly calculated as \$12.85. If the hedge ratio is calculated as 0.7559, then using 10,000 calls, the number is stocks and call required are 7559 shares and 10, 000 calls. EXPLAIN whether you will long or short the stocks/calls.

dont you need to do the tree and reevaluate the call then decide if it’s overpriced or underpriced - decide if you go long or short

yeah… if you go long calls, you short the stock and vice versa… but you’d have to see first if it is over priced or underpriced i think…

i crafted this question from the cfai text Q 4 page 219. THere are those where you havea call price to compare with in this case they dont give they just say go long, and i don’t get it. You may please check and revert. Mumukada…if you dont mind, you may provide our email address so I can talk to you by the side…

Do we need to reevaluate the call? perhaps not. Can you guys explain why we need to reevaluate the call? Problem seems to be quite similar to a delta neutral one. So I guest in this case you long a stock and short a call or short a stock and long a call.

grace: I checked the CFAI text and the original question (4B) asked you to create a “risk free hedge” based on the price of the option you calculated in part A of the question. the answer is to go long 7559 shares and short 10,000 calls in order to earn the risk free rate. As for why to choose to short the calls and long the stock…I’m guessing that because the probability that the stock will rise is about 60% and that the rise is more than a down, the market is assumed to be bullish and therefore the prudent strategy is a covered call position (short calls long stock)…premiums from the short offset any small dips and the upside is unlimited. I checked the section and the only reference to why they would choose a certain arbitrage position was to indicate that such an explanation was beyond the scope of the book (???) the binomial tree shows the call is correctly priced so it’s not a case of arbitrage for profit but rather portfolio insurance as far as I can tell.

shukriya maile, Thanks for the explanation…I take it that in the original derivation of the formular n is the number of units of underlying stocks bought. So unless there is a mispricing of the option, I take it that n is stocks bought/longed. Does read tight but will take that for now until I get a newer and a better revelation