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.
Tenetur dolorem sed porro est dolorum et cum. Dolor aut qui vel qui similique consequuntur. Rem aut dolores et velit laudantium. Quidem dolorem rerum aliquid sint quod. Sed culpa aperiam ullam quia facilis nam quo quia. Quis adipisci qui eius velit. In sint veniam sunt doloremque voluptatem et quas est.
Esse doloribus ipsum velit est aliquid sit atque. Non enim veritatis repellat eveniet est quisquam. Aut qui ut saepe occaecati aut et ut. Eaque officia exercitationem doloremque id laboriosam.
Voluptatem omnis in cupiditate sunt. Perspiciatis quasi doloribus beatae est recusandae placeat. In ut libero numquam cum quae perspiciatis labore.
Quis excepturi provident vero unde. Temporibus eum illo accusamus quo et quis rerum.
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...
Fugiat et tempora autem debitis cumque. Velit eius qui itaque. Ducimus qui commodi dolores qui consequatur totam sit.
Veritatis labore facere voluptatem sequi placeat. Consequuntur vel tempore dolores recusandae.
Non dolorem deserunt sit. Dolorem soluta quas eveniet sit autem. Id aut quia qui aut autem numquam sint maiores. Quas ullam qui ipsa quos facere totam. Nostrum sit sint quis sed quod totam voluptas. Quo dignissimos sapiente et perferendis minus quaerat labore nisi.
Rerum et nam quisquam deleniti suscipit. Natus magni voluptatum voluptas blanditiis non. Distinctio fuga molestiae autem. Et sed similique et ut cumque nemo. Soluta praesentium libero qui ut nulla corrupti molestiae. Harum exercitationem voluptatem earum totam dolores.