QuoteOriginally posted by: lord12r = 0.1 u = 1.2 d=.9. John thinks the stock will go up and makes a bet with Jerry. If S1>S0, John will $100 from Jerry. If S0<S1, John will give $100 to Jerry. Who has the advantage?An idea is the following: five cases for each guy. I think theycan hedge out the risk which depends on the situation of option at that time. The clue is :1) They can not hedge out risk if only hold/sell the stock...In the side of Jerry:1. Jerry can buy X stock(Let us suppose the price is 1) at time 0 , if stock is up, he will get X*1.2-100 ,if stock is down, he will get X*0.9+100. So, he need X*1.2-100>(1+r)*x=1.1X and X*0.9+100>1.1Xto hedge out any risk, 0.1X>100 and 100>0.2X hold at the same time. it is impossible .In the side of John, he need X*1.2+100>1.1X and X*0.9-100>1.1X So X>-1000 and -100>0.2X (X<-500). We get-500<X<-1000! it is impossible if John buy stock. 2) But it seems promising if they can use call/put option to hedge out the risk. Eg: John can sell the call option at time 0 and the strike is K. the call option price per stock is then (1.2-K)*2/3.Suppose he sell X call option to his client, the total money at time 1 is if stock is up, he will get (1+r)*X*(1.2-K)*2/3-(1.2-K)*X+100. So if 100>(1.2-K)*0.27X, he will win 100- (1.2-K)*0.27X bucks.Notice we need X<100/((1.2-K)*0.27) If stock is down, he will get (1+r)*X*(1.2-K)*2/3+(K-0.9)*X-100=> 0.73*(1.2-K)X+KX-0.9X-100,we need 0.23K*X-0.02X-100>0 to get profit, so he needs X>100/(0.23K-0.02) .In this way, we know if 100/((1.2-K)*0.27)>100/(0.23K-0.02)=> 0.23K-0.02>0.32-0.27K=>0.5K>0.34 => K>0.68=> Always hold if we know u=1.2 d=0.9.In this example, if John is a banker, he can bet with Jerry as he can hedge out therisk completely! Any idea?
Last edited by letiand
on April 10th, 2007, 10:00 pm, edited 1 time in total.