Need Help with Options Homework
Having a hard time wrapping my head around these..any help would be greatly appreciated
1) On the 1st of May 2013 you enter a Forward Rate Agreement to borrow on the 1st of September 2013 1,000,000 for 8 months at a fixed annualized interest rate of 5% (for a FRA with a contract length of 8 months the compounding frequency is 1.5 times cpa). Suppose the following bonds are traded in the market on the 1st of August 2013:
-1 month zero coupon with $1000 face value trades for $996.672
-3 month zero coupon with $1000 face value trades for $989.555
-1 year 10% semi-annual coupon bond with $1000 face value currently trades for $1051.706
-1 year 16% quarterly coupon bond with $1000 face value currently trades for $1110.628
-1 year 4% quarterly coupon bond with $1000 face value currently trades for $993.938
What is the value of the FRA for you as a borrower on the 1st of August 2013?
2) Today (time t=0) the stock price of company XYZ is S0 = 70. In 6 months (time t=0.5) it changes (under the true probability measure P) with probability of 70% to S=90 and with probability of 30% to S=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. Using replicating portfolios, what is the price of a European at-the-money call option with 1 year left to maturity?
b. What is the price of an American at-the-money call option with 1 year left to maturity?
c. 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?
At least attempt it before you ask for help. Show what you have so far.
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