Stochastic Calculus and Option pricing,
assignment week 5
Agn`es Tourin
October 9, 2015
Problem: the Heston stochastic volatility model (drawn from the
textbook by Shreve, Stochastic Calculus)
Consider the Heston stochastic volatility model under a risk-n

FRE6233, Assignment 2
Problem 1 (15 points)
Compute the covariance of the Brownian bridge (see slides, second definition).
Problem 2 (25 points) (from the textbook by Shreve) Let W (t) be a brownian motion, and
define
Z t
sign(W (s)dW (s),
B(t) =
0
where

FRE6233, assignment 4 (week 4)
Agn`es Tourin
October 1, 2015
Question 1 (25 points)
We define the forward and futures prices as
F orS (t, T ) =
S(t)
, F utS (t, T ) = E[S(T
)|F(t)].
B(t, T )
1. (5 points) Give B(t, T ) when the interest rate is a constant

FRE6233, Assignment 3, week 3
Question 1 (30 points)
Consider the Black-Scholes framework with the standard notations and a claim of the form
(S(T ) at time T > 0. We assume that the function satisfies the property
(t s) = t (s), t > 0.
1. (5 points) Writ