Valuation of Inflation-Indexed Derivatives Using Path-Dependent Simulation
H. Vermeer (TU Delft - Electrical Engineering, Mathematics and Computer Science)
G.N.J.C. Bierkens – Mentor (TU Delft - Statistics)
Patrick Ruitenberg – Mentor (KPMG Netherlands)
F. Fang – Graduation committee member (TU Delft - Numerical Analysis)
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Abstract
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.