120(0 JOURNAL OF POLITICAL ECONOMY in group A (B)by e,that is,g=e(g4=-e).If we write bo for the value of the option for an agent in group A that buys the asset when g=-e and b,for the value of the option for an agent of group B that buys the asset when g4=e,then bo= h(-e) where h(-e)/h(e)is the discount factor from equation (23).Symmetry requires that bo=b,and hence h(-e) bo= r+入h(e)-h(-) Ase→0， 1h(0) bn 2r+入)h'(0) b. In this illustration,as e0,trading occurs with higher frequency and the waiting time goes to zero.In the limit,traders will trade infinitely often and the small gains in each trade compound to a significant bubble.This situation is similar to the cost from hedging an option using a stop-loss strategy studied in Carr and Jarrow (1990). It is intuitive that when o.becomes larger,there is more difference of beliefs,resulting in a larger bubble.Also,when p becomes larger,for a given level of difference in beliefs,the resale option is expected to be exercised quicker,and therefore there is also a larger bubble.In fact we can show that the following lemma is true. LEMMA 3.If c is small,b increases with o,and p and decreases with r and 0.For all x<k',g(x)=b[h(x)/h(k)]increases with o.and p and decrcases with r and 0. The proof of lemma 3 actually shows that whenever c is small,the cffect of a change in a parameter on the barrier is second-order. Proposition 1 allows us to write o,and p using the parametersφ，入， opi,=o0 and in=oom where i,and ip measure the information in each of the two signals and the dividend flow,respectively.To simplify calculations,we set A 0.Then 0g=2b0 p=(2-中2)+(1-Φ) Differentiating these equations,one can show the following:(1)As o,increases,o.increases and p is unchanged.Therefore,b and g(x),for x<k,increase.The bubble increases with the volatility of the funda- Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission