Option Valuation (Multi-State Approach) [30 Points]
Below is a two-period price tree for a share of stock in Ameren Corp (AEE)

Today In 6 Months In 1 Year
$95.59
$86.90

$79 $82.56


$75.05
$71.30
Using the binomial model, calculate the value today of a call option on AEE stock with a strike price of
$77. You may assume that the 6-month risk-free rate is 3.0%.
To solve this problem you will need to break-up the problem into a number of 2 state models and work
backwards. Let’s go through each of the steps.
(a) Calculate the price of the option 6 months from today (CU) if the stock price were to increase to
$86.90 in 6 months. [10 Points]
(b) Calculate the price of the option 6 months from today (Cd) if the stock price were to decrease to
$75.05 in 6 months. Note: When calculating the hedge ratio round to 4 decimal places. [10 Points]
(c) Calculate the price of the option today (C). (Hint: The value of the call 6 months from now will be
either be Cu (the answer you found in Part (a)) or Cd (the answer you found in Part (b)). Note: When
calculating the hedge ratio round to 4 decimal places. [10 Points]