WW: 1Course: M339W/M389W - Financial Math for Actuaries Page: 1 of 1
University of Texas at Austin
Warm-up worksheet
Prep for “coupled” trees.
Provide your complete solution for the following problem(s):
Problem 1.1. The current price of a continuous-dividend-paying stock is $80 per share. Its prepaid forward
price for delivery at time−1 equals $78.
There are two possible states of the world at the of the one-year period: cloudy and sunny. The stock
price in the case of cloudy state of the world will be $100, while the stock price in the case of the sunny state
of the world equals $75.
Let the price today of a zero-coupon bond redeemable at time−1 be equal to 0.9275.
(i) (10 points) What is the risk-neutral probability associated with the above stock-price tree?
(ii) (5 points) Consider a $78-strike, one-year European call option on the above stock. What is the
price of this option consistent with the above stock-price model?
Instructor: Milica ˇ
Cudina