INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
An RBF approach for oil futures pricing
Project Supervisor : Prof. Ram Jiwari
Harsh Kumar
20112047 Integrated Msc. Applied Mathematics
Table of Content
•
•
•
•
•
•
•
Introduction
Problem Formulation
Introduction to RBF
Using RBF in our solution
Experimental Setup
Results
Future Work
2
Introduction
• The problem of pricing oil futures is a crucial aspect of the
energy market.
• Take Schwartz's model for pricing oil futures as the baseline
and realize the addition of a jump term to the model.
• Present the mathematical formulations of the future price.
• Resulting will be a multi-dimensional PIDE which will require
the use of numerical methods to solve
• Use RBF to solve the pricing problem and present the results
• Bear with the jargon!
3
Problem Formulation
• We start with the Schwartz model and add a jump-diffusion
term
• 𝑑𝑆𝑆𝐶 takes care of the continuous change in price
• 𝑑𝑆𝐽𝑀 takes care of the jump, where p is an independent
Poisson process with density > 0
4
Problem Formulation
• D is a portfolio containing futures 𝐺 = 𝐺(𝑆, 𝑧, 𝑡) the quantity
∆1 of the spot price of oil and ∆2 of convenience yield
• After substituting term and simplifying
• We have our PIDE that we want to solve
• We can also model jumps according to Pareto’s distribution
5
RBF
• Functional approximation technique used to approximate
complex, high-dimensional functions
• There are multiple choices of kernel functions available, we
use Gaussian kernel
• Due to the norm inside, RBF is dimension-blind and hence
useful when we have lot of underlying assets
6
RBF Interpolation
7
Experimental Setup
• Used two datasets, some obtained from real world and some
are simulated
• Restrict the underlying assets to a between 0 to 4.
• Parameter estimation techniques are applied in order to
estimate the parameters of the model such as volatility
• We have used regular discretization for the centres
• Used MATLAB for simulation
8
Results
• Increasing the number of center may lead to smoother
function approximation
• Large number of centers result in higher computational cost
• When using the gaussian kernel, the shape parameter is a
crucial hyperparameter
9
Future Work
•
•
•
•
Understand the behavior of PIDE better
Grasp the use of RBF in the numerical formulation
Study the results of experiments
Implement experiments in python
10
Thank You!
11