MATH 3589 Lecture Notes - Lecture 4: Random Variable, Arbitrage, Risk-Free Interest Rate
1 May 2016
School
Department
Course
Professor
Document Summary
Homework assignment #2 solutions: a stock currently costs per share. In each time period, the value of the stock will either increase or decrease by 50%, and the risk-free interest rate is 10%. Let s0, s1, and s2 be the prices of the stock at times 0, 1, and 2, and suppose we are selling a european-style call option security expiring at time. That is, the value of the option at time 2 is (s2 s1s2)+. (this can be compared with the asian option described in. Exercise 1. 8 in the text; the di erences are that here the strike price is also a random variable, and the average is geometric rather than arithmetic. ) Find the risk-neutral price of this option at time 0. Make sure you draw a tree with all of the branches, distinguishing s2(ht ) and s2(t h), and calculate the price of the option using the formula (s2 s1s2)+ at t = 2.
