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Msf 505 Derivatives Pricing Town Campus Question Paper
Msf 505 Derivatives Pricing Town Campus
Course:Masters Of Science In Commerce
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
EXAMINATION FOR THE MASTERS OF SCIENCE (MSC) IN COMMERCE
(FINANCE AND INVESTMENT)
MSF 505 DERIVATIVES PRICING TOWN CAMPUS
DATE: AUGUST, 2014
TIME: 3 HOURS
INSTRUCTIONS: Answer Question One and Any Other Three Questions
QUESTION ONE (31 MARKS)
(a) Define the term financial derivative and discuss three uses of derivatives
(9 Marks)
(b) Consider a call option on an index with 6 months to expiration and strike price of 100/-.
Suppose the price of the index in 6 months is 90/-.
Find (i) the call pay-off (ii) the purchased call option if the risk-free interest rate is 5%.
(8 Marks)
(c)
Consider the following values: S = 80, K = 75, s= 50%, r = 8%, T = 2 years and d = 0. Let u =
25%, d = 15%, and n = 1. Construct the binomial tree for a call option.
(d)
(9 Marks)
Describe the difference between the over-the-counter and exchange traded derivatives.
(6 Marks)
QUESTION TWO (23 Marks)
(a) Explain the parameters of the Black-Schools option pricing model
(6 Marks)
(b) Suppose the stock price is 120 and the risk-free interest rate is 10%. Draw payoff and profit
diagrams for the following options:
(i) 110 strike put with premium of 3.53
(ii) 110 strike put with premium of 3.26
(iii) 100 strike put with premium of 4.75
(17 Marks)
1
QUESTION THREE (23 Marks)
(a)
Suppose that S follows equation dS = µSdt + sSdZ. Use Itô’s lemma to find the process
followed by G(S, t) = S
(b)
(12 Marks)
Consider the following values: S = 100, K = 95, s= 30%, r = 5%, T = 2 and d = 0. Let u = 1.3,
d = 0.8, and n = 2. Construct the binomial tree for call and put options.
(11 Marks)
QUESTION FOUR (23 Marks)
(a) What is the principle benefit of a binomial option pricing model?
(6 Marks)
(b) Consider a one-period binomial model in which the underlying is at 65 and can go up by 30
percent or down by 22 percent. The risk-free interest is 8 percent.
(i) Determine the price of a European call option with exercise price of 70
(ii) Assume that the call option is selling for 9 in the market. Demonstrate how to execute
an arbitrage transaction and calculate the return. Use 10,000 call options.
(17 Marks)
QUESTION FIVE (23 Marks)
(a) State and explain the assumptions of the Black-Scholes-Merton model.
(8 Marks)
(b) Consider an asset that trades at 400 today. Call and put options on this asset are available with
an exercise price of 400. The option expires in 6 months, and the volatility is 30% per annum.
The continuously compounded risk-free interest rate is 9%.
(i)
Using Black-Scholes-Merton model, calculate the value of call and put options. Assume
that the present value of cash flows on the underlying asset over the life of the options is
4.25
(ii)
Calculate the value of the European call and put options using Black-Scholes-Merton
model. Assume that the continuous dividend yield is 1.5%.
(15 Marks)
QUESTION SIX (23 Marks)
(a)
An analyst wants to study the trend and fluctuation of price of an asset in a given market. The
following is the sequence of the daily price of the underlying asset for last month:
2
Date price Date price
1 159 13 162
2 157 14 161
3 160 15 160
4 161 16 161
5 160 17 163
6 161 18 164
7 159 19 166
8 157 20 167
9 157 21 166
10 156 22 165
11 159 23 162
12 160 24 170
The analyst is required to advice using the mean return and the historical volatility.
Calculate the return and historical volatility of underlying
(b)
(16 Marks)
State and discuss three option Greeks (5 Marks)
3
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