MENU
Stan Loper is unfamiliar with the Black-Scholes-Merton (BSM) option pricing model and plans to use a two-period binomial model to value some call options. The stock of Arbor Industries pays no dividends and currently trades for $45. The up-move factor for the stock is 1.15, and the risk-free rate is 4%. He is considering buying two-period European style options on Arbor Industries with a strike price of S40. The delta of these options over the first period is 0.83.
Loper is curious about the effect of time on the value of the calls in the binomial model, so he also calculates the value of a one-period European style call option with a strike price of 40.
Loper is also interested in using the BSM model to price European and American call and put options. He is concerned, however, whether the assumptions necessary to derive the model are realistic. The assumptions he is particularly concerned about are:
* The volatility of the option value is known and constant.
* Stock prices are lognormally distributed.
* The continuous risk-free rate is known and constant.
Loper would also like to value options on Rapid Repair, Inc., common stock, but Rapid pays dividends, so Loper is uncertain what the effect will be on the value of the options. Loper uses the two-period model to value long positions in the Rapid Repair call and put options without accounting for the fact that Rapid Repair pays common dividends.
The value of the one-period European style call option is closest to:
The payoff is zero for a down-move and 11.75 for an up-move. Since the probability of
an up-move is 0.607 the present value is
(Study Session 17, LOS60.b)