1.

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.

3.
The assignment must be submitt ed in the Library with a completed University coversheet on the due date.

4.
The assignments submitted for grading can be word processed or handwritten. There is NO penalty for handwritten assignments.

5.
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.

The term
structure is flat, with all risk

–
free interest rates being 10%.

a.
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?

b.
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.

b.
Use a two-step binomial tree to calculate the value of a six-month American put option with a strike price of $42.

c.
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.

Problem
4
: 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]