In an arbitrage-free market, there are two time intervals and random interest rates between time 2 and time 3. Assume that an asset would pay no dividends during these two intervals. Each row of the following table shows a possible evolution of asset prices from time 1 to time 3.
EVOLUTION OF ASSET PRICES
|
Time 1 |
Time 2 |
Time 3 |
|
$5 |
$6 |
$8 |
|
$5 |
$6 |
$5 |
|
$5 |
$3 |
$5 |
|
$5 |
$3 |
$3 |
The interest rate between time 1 and time 2 is 10%; the interest rate for the first two situations between time 2 and time 3 is 12%, and 8% for the last two situations.
- Calculate all the risk-neutral probabilities between time interval 1 and 2 as well as time interval 2 and 3.
- Calculate the future and future prices.