A1.1 (i) Implement a Matlab function for the down-and-out call option for (H  X) (see John
Hull's chapter on exotic options):
Cdo = C 􀀀 Cdi
where
Cdi = S0e􀀀q (H=S0)2N(y) 􀀀 Xe􀀀r (H=S0)2􀀀2N(y 􀀀 
p
 )
with
 C: the Black-Scholes call option price,
 q: the continuous dividend rate,
 H: the barrier level,
 S0: current underlier price,
 X: strike price,
  : time to maturity, in years,
 r: risk free rate,
  =
r 􀀀 q + 2=2
2 ,
 y =
ln[H2=(S0X)]

p

+ 
p
 .
(ii) Consider a down-and-out option which has a time to maturity of 0.5 year, strike price
of $52, barrier level of $50, its underlier has a current price of $55, volatility of 40%,
dividend yield of 2%, and the risk free rate is 5%. Implement the Binomial Tree Method
for pricing a given down-and-out option. Use your Matlab functon to compute Cdo for
the number of time periods 10, 100, 500, 1000, 5000 and 10000 respectively. Comment
on your answer.
(iii) Use Boyle and Lau's method to obtain the value of N (the number of time periods) for
which the actual barrier is closest to state level j = 29. Use Matlab to numerically verify
that the errors incurred for this value of N is indeed minimized compared to those for
adjacent values of N.

A1.2 (i) Use a Matlab function to implement the single-state variable binomial lattice method
for computing prices of an American
oating strike lookback put option (newly issued)
which has a time to maturity of 0.5 year. The underlier has a current price of $50,
volatility of 30%, dividend yield of 3%, and the risk free rate is 2%. Obtain the estimates
to the option value for number of time steps being 10, 100, 1000 and 10000 respectively.
Comment on your answer.
(ii) Modify your implementation of the lookback program in A1.2(i) so that it can handle
options which are not newly issued and has a running maximum more than S0. Test
your implementation with the same option parameters and the numbers of time steps
as in A1.2(i) but this time with a running maximum of $53. Use linear interpolation
where appropriate. Comment on your answer.


A1.3 (i) Implement the two-state-variable forward shooting grid method as a Matlab function
for estimating prices of a European xed strike arithmetic Asian call option.
(ii) Use your Matlab function in A1.3(i) to estimate the price of a European xed strike
arithmetic Asian call option which has a time to maturity of 0.5 years, a strike price of
$19, and a underlier which has a current value of $20, volatility of 40%, dividend yield
of 2%, running average of $21, and the risk free rate is 5%. Take  = 1=2. Use linear
interpolation where appropriate. Present results with the number of time steps for the
FSGM being 50, 100 and 200, and assuming that the running average was taken for 25,
50, and 100 time steps previously. Comment on your answer.

A1.4 (i) Implement the two-state-variable forward shooting grid method as a Matlab function
for estimating prices of a European xed strike lookback call option.
(ii) Use your Matlab function in A1.4(i) to estimate the price of a European xed strike
lookback call option which has a time to maturity of 0.5 years, a strike price of $19,
and a underlier which has a current value of $20, volatility of 40%, dividend yield of
2%, running maximum of $23, and the risk free rate is 5%. Use linear interpolation
where appropriate. Present results with the number of time steps being 50, 100 and
200. Comment on your answer.
././ The End ././