Answer all questions.
2.You need to provide adetailed,clearly-arrangedsolution of all questions
. Providing merely a number as a result without showing how you have obtained this result will lead
to 0 marks for the corresponding question
. Using tables and diagrams may be helpful for providing clearly-arranged solutions.
The assignment must be submitt ed in the Library with a completed University coversheet on the due date.
The assignments submitted for grading can be word processed or handwritten. There is NO penalty for handwritten assignments.
Late submissi on will attract a deduction of 2 marks per day for penalty.
What is the lower bound for the price of this call?
b.Assume that the call is currently selling for $3.
Describe in detail with which strategy you can gain an arbitrage profit and how much this profit will be.
Problem 2:Properties of Options
The price of a European call that expires in six months and has a strike price of $50 is $5. The
underlying stock price is $52, and a dividend of $1.00 is expected in three months.
structure is flat, with all risk
free interest rates being 10%.
What is the price of a European put option on the same stock that expires in six months
and has a strike price of $50?
Explain in detail the arbitrage opportunities if the European put price is $0.50.
How much will be the arbitrage profit?
Problem 3: Binomial Trees
A stock price is currently $40. Over each of the next two three month periods it is expected to go
up by 10% or down by 10%. The risk-free interest rate is7% per annum with continuous compounding
a.Use a two-step binomial tree to calculate the value of a six-month European put option with a strike price of $42.
Use a two-step binomial tree to calculate the value of a six-month American put option with a strike price of $42.
Use a two-step binomial tree to calculate the value of a six-month European call option with a strike price of $42.
d.Show whetherthe put-call–parity holds for the European put and the European call.
: Binomial Trees A stock price is currently $30. During each two
month period for the next four months it isexpected to increase by 8% ord ecrease
by 10%. The risk-free interest rate is 5%. Use a two-steptree to calculate the value of a derivative that pays off 2max[(30 ) 0]