# Software Listing of Author : "Ahmos Sansom"

Introduction ---------------- This code simulates commodity spot prices using the Clewlow and Strickland one factor daily spot model using a Monte Carlo approach. The derived stochastic differential equations (SDEs) are solved using several finite difference schemes. The paper detailing the equations is available online in ref 1 below. The example requires a commodity forward curve and assumes a one factor volatility model of the form sigma = A exp(-c(T-t)), where A is the cash volatility, c is the mean reversion rate and T is the maturity. The code highlights several different finite difference schemes to solve the spot equation applied using a Monte Carlo appraoch. Numerical finite difference schemes 1 = Euler log transformation 2 = Euler scheme 3 = Semi implicit Euler log transformation 4 = Weak predictor/Corrector on log...

• Platform: Matlab, Scripts

Solves nonlinear diffusion equation which can be linearised as shown for the general nonlinear diffusion equation in Richtmyer & Morton [1]. The approach is to linearise the pde and apply a Crank-Nicolson implicit finite difference scheme to solve the equation numerically. Matlab run command -------------------------- type: IsoFreeSurfaceSolver solves the pde: ------------------- frac{partial h}{partial t}=frac{1}{12}frac{partial^2 h^4}{partial x^2} The pde has the application to isothermal viscous fluid flow spreading on a horizonatal substrate under gravity - Huppert [2]. Note that PDE has been nondimensionlised. Initial conditions: t=0: h = (1 - x^2)_{+} + 10^-6 (has prewetting film) The spatial domain is discretised taking account of symmetry at x = 0: frac{partial h}{partial x} = 0 and is also used to close the...

• Platform: Matlab, Scripts

The solution of the nearest correlation matrix applies the hypershpere or spectral decomposition methods as outlined in Monte Carlo methods in Finance by Peter Jackel, Chapter 6. Use CorrelationExample.m that applies a simple example for the two cases.

• Platform: Matlab, Scripts

This code optimises the parameters for the term structure of volatility (TSOV) applied to historical forward curves - see discussion in Harris in reference 1 below. TSOVs avaible are: TermType - 1 = sigma = A exp (-CT) - 2 = sigma = A exp (-CT) + D - 3 = sigma = (A + BT) exp (-CT) + D Required data - Local volatility and return data - both assumed annualised. The optimisation applies the nonlinear least square fitting tool and MLE approach using the fminsearch function - see reference 2. To run type: TSOVControl This code can be used to derive TSOV parameters for the Clewlow and Strickland Forward curve or spot models. References 1. "Electricity Markets, - Pricing, Structures and Economics, " Chris Harris, Wiley, 2006. Discussion on MLE vs. FMINSEARCH 2....

• Platform: Matlab, Scripts

Simple example showing how a value neutral hedge is determined for the UK power (electricity) markets. HedgeControl Function for power hedging of Balance of Month, Monthly and Seasonal products based on value forward preservation hedging, i.e. uses the forward curve to determine the value neutral hedge. The code assumes that there is limited liquidity and that only Base, Peak and Night products are only available to hedge the demand profile. To run: HedgeControl

• Platform: Matlab, Scripts
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