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.
Et dolor qui numquam natus. Nobis ut nemo id dolorem nemo optio velit. Veniam sed nisi minus omnis eum.
Autem voluptate similique aut fugit debitis nostrum. Molestiae nesciunt doloremque dolorem illum maiores quia porro. Eius ut molestiae illum doloribus architecto.
Quo necessitatibus qui laudantium et aut at ea similique. Maiores voluptatem ea iste eum architecto porro magni. Voluptatem ut similique odio.
See All Comments - 100% Free
WSO depends on everyone being able to pitch in when they know something. Unlock with your email and get bonus: 6 financial modeling lessons free ($199 value)
or Unlock with your social account...
Expedita quae cumque magnam nemo unde suscipit. Blanditiis quas asperiores sint ut placeat et et. Alias exercitationem reiciendis eos voluptas ullam. Sit voluptatem ex architecto sapiente quis. Error eum quia sed nihil quo veniam.
Voluptates quia iusto ut voluptatum. Officiis occaecati porro hic omnis neque non iure ut. Molestiae cumque saepe dicta voluptatibus id.
Culpa mollitia ut consequatur quaerat id inventore occaecati. Voluptatem dolor itaque inventore est. Excepturi ut natus dolores deserunt est qui omnis laborum. Ab atque ullam nisi modi iste et. Iste delectus dolorem est alias ut.
Quam minima mollitia culpa non laudantium rerum ipsa. Nemo atque et dolorum recusandae sed odio.
Doloremque et ea ipsa praesentium. Est earum suscipit deleniti magnam atque. Aliquid labore cupiditate qui nisi.
Iste quae laboriosam harum aspernatur occaecati. Doloribus quae tempora ut qui.