4 questions needed ASAP

Sep 14th, 2014
Business & Finance
Price: $20 USD

Question description

Question 1(4 marks)

Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months.

a)What is the price of the option if it is a European call?

b)What is the price of the option if it is an American call?

c)What is the price of the option if it is a European put?

d)Verify that put-call parity holds.

Question 2(4 marks)

The current price of a non-dividend-paying biotech stock is $140 with a volatility of 25%. The risk-free rate is 4%. For a three-month time step:

a)What is the percentage up movement?

b)What is the percentage down movement?

c)What is the probability of an up movement in a risk-neutral world?

d)What is the probability of a down movement in a risk-neutral world?

Use a two-step tree to value a six-month European call option and a six-month European put option. In both cases the strike price is $150.

Question 3(3 marks)

A one year European put option and a one year European call option with a strike price of $59 are both priced at $5 in the market a one year futures price is currently traded at $58. The risk free rate is 7% per annum. Is there an arbitrage opportunity, if so, show the gain on the arbitrage.

Question 4(4 marks)

A financial institution has the following portfolio of over-the-counter options on sterling:



Delta of option

Gamma of option

Vega of option





















A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.

a)What position in the traded option and in sterling would make the portfolio both gamma neutral and delta neutral?

b)What position in the traded option and in sterling would make the portfolio both vega neutral and delta neutral?

Tutor Answer

(Top Tutor) Daniel C.
School: Rice University

Studypool has helped 1,244,100 students

Review from our student for this Answer

Sep 22nd, 2014
"Top quality work from this guy! I'll be back!"
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1824 tutors are online

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors