Comment on the following statements17 :

(a)

Wilmott (2007, p. 77): Assume: “(1) two stocks A and B; (2) both have the same value, same volatility and are denominated in the same currency; (3) both have call options with the same strike and expiration; (4) stock A is doubling in value every year, stock B is halving. Therefore, both call options have the same value. But which will you buy? That one stock is doubling and the other halving is irrelevant. That option prices don’t depend on the direction that the stock is going can be difficult to accept initially”.

(b)

Ross (1998, p. 701): “Take two stocks that both follow binomial processes and that are not perfectly correlated. Further, suppose that the stocks differ only in that one has a much higher probability of an up jump than does the other. If our analysis is to be believed, then when the stock prices of each are equal the two option values will be equal! How can this be? How can the value of an option on a stock be independent of the probability that the stock will go up?”.