First consider a call option that expires 37.4

one year from now on stock ABC, which /

does not pay any dividends. The 31.3

possibilities for the price of the / \

stock over the next year are as 25.2 25.4

shown in the tree diagram on the \ /

right. The riskfree interest rate 19.3

is 7.10%, compounded semiannually. \

The striking price of the option is $26.20. 13.4

1. Suppose the price of ABC stock six months from now turns out to be $31.3.

What then (six months from now) would be the optimal hedge ratio for an

arbitrageur writing a call option that expires one year from now?

2. If the price of ABC stock is $31.3 six months from now, what then

would be the no-arbitrage price of the call option?

3. Suppose instead that the price of ABC stock six months from now turns out

to be $19.3. What then would be the optimal hedge ratio for an

arbitrageur writing a call option that expires one year from now?

4. If the price of ABC stock is $19.3 six months from now, what then

would be the no-arbitrage price of the call option?

5. What is the optimal hedge ratio for an arbitrageur writing

a call option today that expires one year from now? (Remember, the current

time is one year before expiration and the price of ABC equals $25.2.)

6. What is today's no-arbitrage price of the call option? (Remember, that

today is one year before expiration and the price of ABC equals $25.2.)