Coursework 2 - MATH3734 /5734M
This piece of coursework is worth 15% of the final module mark and it is marked out
of 20.
You need to solve the problems on the Excel template provided and to submit your
solutions via Turnitin on Minerva.
Deadline for submission is Wednesday 5 May at 2 pm. Late submission will be
penalised: 25% off if submitted by Thursday 6 May at 2 pm, no marks after that.
Problems
Problem 1 (10 marks). Let (Wt )t≥0 be a one-dimensional Wiener Process. For con-
stants r, σ, s0 > 0, consider the stochastic process
St = s0 exp
(
(r − σ
2
2
)t + σWt
)
.
Simulate 500 independent copies of ST and use the Monte Carlo Method in order to
estimate the two quantities
• E[(ST − K)+]
• E[(K − ST )+],
for the choice of parameters T = 1,r = 0.1, σ = 0.1, s0 = 100,K = 120. Recall that for
a real number x, we set x+ = max{x,0}.
Problem 2 (10 marks). Let b ∈ R and consider the stochastic process (X)t≤2 which is
given as the unique solution of the equation
dXt =
1
5
Xt dt + b dWt, X0 = 1, t ∈ [0,2].
By using the Euler scheme with step size 1/100, simulate 3 paths of the process (X)t≤2
for b = 1 and plot them in the same graph. On the separate sheets of the template, do
the same for each of the choices b = 0.2,0.1,0.01. What do you observe (state it in the
last excel sheet)?
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