FIN3017
Exam Time Table Code FIN3017
Normal answer book
Formula sheet and tables attached
Approved calculators only
LEVEL 3
EXAMINATION FOR THE DEGREE OF
BACHELOR OF SCIENCE (FINANCE)
AND OTHER DEGREES
FINANCIAL ENGINEERING
Thursday, 12th January 2017 9:30 AM - 11:30 AM
Examiners: Professor Gerhard Kling
and the internal examiners
Write on both sides of the answer paper
Answer ALL three questions
All questions carry equal marks
Allocation of marks within questions is shown
You have TWO HOURS to complete the paper
FIN3017

Answer ALL three questions

1. (a) Construct a two portfolio strategy to establish the put-call parity
relationship for an option on a non-dividend paying share.

(20 Marks)

(b) You are presented with the following information:

S0 = £1.25; X = £1.30; T = 2 months; r = 0.03 (continuously-
compounded); Call option price (C) = £0.15; Put option price (P) =
£0.25.


(i) Demonstrate that there is mispricing of the option contracts

(ii) Construct an arbitraged based strategy to take advantage of
this mispricing.

(20 Marks)

(c) You are presented with the following information:

Nissan car company wishes to borrow €50m USD for 5 years;

Air Berlin wants to borrow 5,650m Yen for 5 years;

The current EUR/JPY exchange rate is EUR = 113 JPY

The two companies have been offered the following loan rates

Yen (¥) EUR (€)
Nissan car company 2.0% 3.0%
Air Berlin 3.8% 4.0%
Design a swap that will provide a bank, acting as an intermediary,
0.1% per annum and which divides the remaining gains in the swap
equally between the two companies


(20 Marks)

(d) (i) What is meant by the term Swap Spread?

(ii) The UK 10 year swap spread was –2.4 basis points on the
12thOctober 2016 what did this imply about market interests?

(20 Marks)

(e) Detail the purpose and the features of a Credit Default Swap. (20 Marks)

(Total 100 Marks)
Page 2 of 8
FIN3017

2. (a) Which of the following models is most appropriate as a description of
stock price behaviour? Give reasons for your answer.


(i) ds=dt + dz

(ii) ds= sdt + dz

(iii) ds=dt + sdz

(iv) ds= sdt + sdz

( and  are constants and dz represents a Wiener process) (20 Marks)

(b) Explain the no-arbitrage approach to valuing a European option using
a one-step binomial tree.

(20 Marks)

(c) Consider a European put option on a non-dividend-paying stock
where the stock price is £2.50, the strike price is £2.50, the risk-free
rate of interest is 2% per annum, the volatility is 20% per annum, and
the time to maturity is six months.


(i) Calculate u , d , and p for a two time step tree

(ii) Value the option using a two time step tree.

(iii) Calculate and interpret the delta and gamma option price
sensitivities at the second time step

(30 Marks)

(d) Explain the importance of the lognormal property of stock prices in
the derivation of the Black-Scholes stock option pricing model.

(20 Marks)

(e) Why are employee stock options more difficult to price than standard
call option contracts?

(10 Marks)

(Total 100 Marks)
3. (a) Analysts at times calculate measures of the contribution of sub-
portfolios to the overall portfolio Value at Risk (VaR). Explain this
statement with reference to (i) Marginal VaR, (ii) Incremental VaR and
(iii) Component VaR.
(20 Marks)

(b) Explain the key features of the delta normal approach in the
computation of Value at Risk (VaR) for a portfolio of options.

(20 Marks)

(c) Consider a position consisting of a £5 million investment in HSBC Plc
and a £3 million investment in BP Plc. Suppose the daily volatilities
of these two assets are 1.3% and 2.6% respectively and that the
coefficient of correlation between their returns is 0.39. What is the
10-day 99% VaR for the portfolio? By how much does diversification
reduce the VaR?
(20 Marks)


Page 3 of 8
FIN3017

(d) The spread between the yield on a 5-year corporate bond and the
yield on a similar risk-free bond is 95 basis points. The recovery rate
is 45%. Estimate the average default intensity per year over the 5-
year period.

(20 Marks)

(e) Explain the difference between an unconditional default probability
density and a hazard rate.

(20 Marks)

(Total 100 Marks)

END OF EXAMINATION
Page 4 of 8
FIN3017

FORMULA SHEET

(i) For an investment asset, the futures price is:

0 0
cTF S e

where c is the cost of carry.


(ii) For a consumption asset, the futures price is:

( )
0 0
 c y TF S e

where y is the convenience yield.


(iii) The price of a bond is given as:

1



n
yti
i
i
B c e

where y is the yield, continuously compounded.


(iv) The duration of a bond is given as:

1


 
  
 

ytin
i
i
i
c e
D t
B



(v) A measure of convexity is:

22
1
2
1

 
 i
n yt
i ii
C t ed B
C
B Bdy



(vi) For the binomial model the probability of an up movement is p and it is given by:




a d
p
u d



Page 5 of 8
FIN3017


where
1





r t
t
a e
u e
d
u


(vii) The option price can be written as:

 (1 )  rT u df e pf p f

(viii) Black-Scholes formula (call)

( )
1 2( , ) ( ) ( )
r T tC s t SN d Ke N d  

2
1
ln( ) ( )( )
2
S
r T t
Kd
T t


  




2
2
ln( ) ( )( )
2
S
r T t
Kd
T t


  

 (ix) Black-Scholes formula (put)


( )
2 1( , ) ( ) ( )
r T tP S t Ke N d SN d    

2
1
ln( ) ( )( )
2
S
r T t
Kd
T t


  




2
2
ln( ) ( )( )
2
S
r T t
Kd
T t


  

