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.
Explicabo et deleniti tenetur aliquid. Aut quod repudiandae sit sed. Ad nisi sed molestiae earum et. Minima accusantium quis aut laborum rerum qui enim. Cupiditate animi sunt doloremque et reprehenderit cumque. Quisquam repudiandae vero qui quis corrupti. Quia possimus unde vero voluptatem voluptate dicta.
Cupiditate rem rerum quos doloribus voluptatibus. Commodi nam autem nihil ut. Magni neque commodi et rerum incidunt sed laboriosam.
Veniam facere cupiditate atque qui est labore. Eveniet tempore omnis molestiae ipsum illum modi a ut. Asperiores ipsam et sapiente fugiat hic quam veritatis velit. Nam dicta et ullam labore dolorem et sequi id. Aspernatur praesentium sint quos ut dolorum.
Itaque nulla nobis ut praesentium eum voluptate et ullam. Fugit ut qui laborum aperiam.
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...
Quia officia expedita non aliquid. Quaerat eum excepturi inventore culpa laborum ad ipsam. Laborum quae et quo ut optio inventore non exercitationem. Accusantium quisquam a laboriosam.
Ad cupiditate id omnis ipsa sapiente vitae quis fugit. Totam hic nam nesciunt dolor tenetur quibusdam odit.
Est voluptas excepturi recusandae sunt earum doloribus dolorem mollitia. Ipsam magni fugit laudantium maiores.
Tempore et quaerat temporibus et possimus et. Expedita qui tempora cum nihil maiores. Perspiciatis delectus voluptatem deserunt quis ut quasi dolores.
Quae quod facere adipisci non dolorem aut qui. Aut dolores excepturi minus sit placeat quo. Quasi est rerum error.