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Project 2 (50% of the final mark)
Path dependent options pricing
using object-oriented programming
C++ Programming with Applications to Finance Spring 2021
The aim of this project is to create a program in C++ that can be used to study the prices of Path
Dependent on an underlying asset driven by a binomial model in discrete time. Your program
should be accompanied by end-user and developer documentation. The project is aimed at testing
your knowledge from the Term 2 of the course and must be implemented in the object-oriented
programming paradigm. You must use object-oriented approach when creating this project.
A path dependent option is an exotic option that's value depends not only on the price of the
underlying asset but the path that asset took during all or part of the life of the option.
(source: Investopedia)
We assume that the price of the underlying is strictly positive at moment 0 (S0 = S(0) > 0) and at
each moment t in can either move up (1+u) times or down (1+d) times. As always in the binomial
model there is a risk-free security growing by a factor (1+r) during each time step. For more
details on binomial model please see Capinski & Zastawniak (2012) pp. 1-2.
Further we use S(t) for the price of the underlying asset at moment t, K for the strike, T for
maturity and A(0,T) for the average price for the period [0, T].
You should create a project that includes pricing of four types of path dependent options: a
lookback option, a fixed strike Asian call option (with arithmetic average), a Parisian option and
the one that we will refer to as Consecutive Growth option.
A lookback option is a path dependent option where the option owner has the right to buy the
underlying instrument at its lowest price over some preceding period:
( ( ) ( ))
0
min lookback t T
C S T S t
? ?
= −
. Pleases notice that the minimum is taken over all
t T ??0, ?.
Fixed strike Asian call payoff is given by
C A T K Asian Call = − max 0, , 0 ( ( ) ) , where A(0,T) stands
for arithmetic mean
( ) ( )
1
1
0,
T
t
A T S t
T =
= ? .
The payoff of a standard Parisian option is dependent on the maximum amount of time the
underlying asset value has spent consecutively above or below a strike price
( ) ( ) ( )
( ) ? ? ( )
, 1 ,...,
max 1 , 0,
0,
S s K S s K S t K
Parisian
t s if t T such that S t K
C
otherwise
? + ? ?
? − + ? ? ? ?
= ?
??
. Notice that we
consider the maximal number of consecutive moments (not the periods between the moments)
when the price S(t) of the underlying is at or above some strike value K, and the payoff equals the
number of the moments in such streak. If at all moments from 0 to T the price S(t) is below K (i.e.,
S(t)

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