## Solution Library

# Calculation of Probability of Increase in Stock Price of a company

**Question**

Today (time t = 0) the stock price of company XYZ is S = 70. In 6 months (time t = 0:5) it changes (under the true probability measure P) with probability of 70% to S(u)0.5 = 90 and with probability 30% to S(d)0.5 = 60. From time t = 0:5 to time t = 1 the stock price may increase by 30% with a probability of 50% or decrease by 20% with a probability of 50%. The risk free interest rate is constant and equal to 5% (c.c.).

(a) Draw a tree.

(b) Use replicating portfolios to calculate the price of a European at-the-money call option with 1 year left to maturity.

(c) What is the price of an American at-the-money call option with 1 year left to maturity?

(d) Suppose you own 10 stocks of company XYZ. At time t = 0, how many long or short positions do you have to take in European at-the-money call options with 1 year to maturity if you like to hedge your entire exposure to stock price fluctuations?**Summary**

The question belongs to Statistics and it is about calculation of probability of increase in stock price of a company. By using American and European at the money call options have been calculated. These and other calculations about the stock prices of the company have been calculated.

**Total Word Count NA**

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