A vital aspect of managing inflation risk is the use of inflation-indexed derivatives. Currently, inflation-indexed bonds and swaps are the primary instruments purchased by institutions. Inflation options (also known as inflation caps/floors) are also available in the market. Risk-neutral pricing of these derivatives is a difficult challenge due to the connection between inflation and interest rates.

In this thesis, the Heston model and its extensions to stochastic interest rates are investigated in the context of inflation-indexed derivatives. First, existing analytical pricing formulas and simulation methods are summarized. Then the multilevel Monte Carlo (MLMC) method is applied as a potent variance reduction technique. For the standard Heston model, the MLMC method reduces the computation costs by a factor of 10 to 50 for short maturities. The Python code implementing the applied methods is also published.

The amount of data being produced is growing exponentially. An im-
portant challenge is to find methods to store this data efficiently and in an
environmentally friendly way. One idea that is a growing research topic in-
volves using synthetic DNA. DNA has the potential to be more efficient and
environmentally friendly than current methods. DNA is made of a sequence of
four nucleotides, Adenine (A), Cytosince (C), Guanine (G), and Thymine (T).
To store data, DNA strands can be created with specic nucleotide sequences.
In the process of reading and storing data substitution errors can occur. Two
constraints are introduced to minimise the number of errors. The GC-weight
constraint which states that every DNA sequence must have a fixed number
of G and C nucleotides, and the runlength constraint, which states the maxi-
mum number of repeating nucleotides possible in every DNA sequence.