Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Local sensitivity analysis of heating degree day and cooling degree day temperature derivatives prices

Sara Ana Solanilla Blanco

Abstract

We study the local sensitivity of heating degree day (HDD) and cooling degree day (CDD) temperature futures and option prices with respect to perturbations in the deseasonalized temperature or in one of its derivatives up to a certain order determined by the continuous-time autoregressive process modelling the deseasonalized temperature in the HDD and CDD indexes. We also consider an empirical case where a CAR process of autoregressive order 3 is fitted to New York temperatures and we perform a study of the local sensitivity of these financial contracts and a posterior analysis of the results.

Local sensitivity analysis of heating degree day and cooling degree day temperature derivatives prices

Abstract

We study the local sensitivity of heating degree day (HDD) and cooling degree day (CDD) temperature futures and option prices with respect to perturbations in the deseasonalized temperature or in one of its derivatives up to a certain order determined by the continuous-time autoregressive process modelling the deseasonalized temperature in the HDD and CDD indexes. We also consider an empirical case where a CAR process of autoregressive order 3 is fitted to New York temperatures and we perform a study of the local sensitivity of these financial contracts and a posterior analysis of the results.
Paper Structure (6 sections, 7 theorems, 64 equations, 14 figures)

This paper contains 6 sections, 7 theorems, 64 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Sensitivity of CDD and HDD derivatives prices with measurement period
  3. Sensitivity of CDD and HDD derivatives prices with a measurement day
  4. Empirics
  5. Sensitivity of CDD futures prices with measurement over a period
  6. Conclusions

Key Result

Proposition 2.1

Let $t\leq \tau_1$, then for $i=1,\ldots,p$ it holds that

Figures (14)

  • Figure 1: Expected value of $Z(t,s)$ (complete line) as a function of $s-t$ with measurement day $s$ being August 1st, 2011. In addition, we have inserted the bounds for $\pm1$ std (slashed line) and $\pm2$ std (dotted line).
  • Figure 2: $\Phi(\mathbb{E}_{Q}(Z(t,s)))$ (complete line) as a function of $s-t$, where we have chosen $s$ as August 1st, 2011. In addition, we have inserted $\Phi(\mathbb{E}_{Q}(Z(t,s))\pm i\,\text{std})$ for $i=1$ (slashed line) and $i=2$ (dotted line).
  • Figure 3: $\partial\widetilde{F}_{\text{CDD}}(t,s,\texttt{x}_1,\ldots,\texttt{x}_p)/\partial\texttt{x}_i$ for $i=1,2,3$ as a function of $s-t$ with measurement day $s$ being August 1st, 2011.
  • Figure 4: $(\partial F_{\text{CDD}}(t,s,\texttt{x}_1,\ldots,\texttt{x}_p)/\partial\texttt{x}_i)_{\vert_{\mathbf{x}=\mathbf{0}}}$ as a function of $s-t$ with measurement day $s$ being August 1st, 2011.
  • Figure 5: The relative error in percent between $\partial\widetilde{F}_{\text{CDD}}(t,s,\texttt{x}_1,\ldots,\texttt{x}_p)/\partial\texttt{x}_i$ and $(\partial F_{\text{CDD}}(t,s,\texttt{x}_1,\ldots,\texttt{x}_p)/\partial\texttt{x}_i)_{\vert_{\mathbf{x}=\mathbf{0}}}$ for $i=1,2,3$ as a function of $s-t$ with measurement day $s$ being August 1st, 2011.
  • ...and 9 more figures

Theorems & Definitions (14)

  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Proposition 2.3
  • proof
  • Proposition 3.1
  • proof
  • Proposition 3.2
  • proof
  • ...and 4 more