RISK MANAGEMENT & VALUATION OF ELECTRICITY DERIVATIVES

Risk Management and Valuation of Electricity Derivatives

ABSTRACT

The aim of the Black-Scholes investigation is to find 'fair' charges for derivatives, securities, or commodities. An equitable cost lives, if it is comprehensive to both purchaser and trader and if it is founded on market information. In primary, the Black-Scholes-Merton form is not anything additional than the submission of the present worth to unsecure earnings forecasts. I.e. the worth of a call is founded on the present worth from profits, weighted by their likelihood of incident and their location cost and hit price. To eradicate the flaws cited previous, it is essential to change the Black-Scholes formula. For this reason we adapt the instability component of the aforementioned Black-Scholes formula. Generally, it is factual that there is a inclination in the direction of expanding instability the longer the time gap gets. The linearly boost of the variance is matching to the benchmark deviation.

Table of Content

ABSTRACTII

CHAPTER 01: INTRODUCTION1

Goals of the Black-Scholes-Merton Model1

Conditions for the validity of the Black-Scholes-Merton Model1

a) Geometric Brownian motion1

b) Wiener process2

c) Additional Assumptions of the Black-Scholes Model4

CHAPTER 02: THE ELECTRICITY MARKET5

Derivation5

a) The Geometric Brownian motion5

b) ITOS Lemma5

c) Construction of a Risk-Free Portfolio of Stocks and Options5

d) The Black-Scholes-Differential Equation in More Detail7

e) Simplified Application of the Black-Scholes Evaluation According to the8

Characteristics of the Black-Scholes Solution10

Adaption of the Black-Scholes Formula on Commodity-Futures of the Energy Sector11

Black-Scholes formula for the Evaluation of EEX-Options11

Modification of the Black-Scholes Formula12

CHAPTER 03: RISK MANAGEMENT WITH ELECTRICITY DERIVATIVES14

Delta14

Delta-Hedging16

Example:17

Gamma17

Theta19

Vega20

Rho20

Combination of the Black-Scholes-Formula with the Greeks for rating an option21

CHAPTER 04: VALUATION OF ELECTRICITY DERIVATIVES23

Example for the calculation of sensitivity key figures of a “call option” on a “future-baseload” for electricity23

a) Fair value of the “call future option”23

b)Delta of the “call option”24

c)Gamma of the “call option”24

d)Theta of the “call option”25

e)Vega of the “call option”25

f)Rho of the “call option”25

CHAPTER 05: CONCLUSION27

REFERENCES28

END NOTES30

CHAPTER 01: INTRODUCTION

Looking at the Black-Scholes-Merton Model, it is used as an evaluation procedure for all types of derivates as well as for every type of option application.

Goals of the Black-Scholes-Merton Model

The aim of the Black-Scholes analysis is to find 'fair' prices for derivatives, securities, or commodities. A fair price exists, if it is comprehensive to both buyer and seller and if it is based on market information. In principal, the Black-Scholes-Merton model is nothing else than the application of the present value to unsecure profit forecasts. I.e. the value of a call is based on the present value from earnings, weighted by their probability of occurrence and their spot price and strike price. (Strauss 2003:175-195)

Conditions for the validity of the Black-Scholes-Merton Model

This model postulates that the stock price follows the so-called Geometric Brownian motion.

a) Geometric Brownian motion

The Geometric Brownian motion finds its origin in physics. It can be used to describe the movement of particles that are colliding frequently. This method is also based on the Markov-process which claims that historic market values are not relevant for the price development of stocks, for example. Instead, only the current value determines its future ...