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The Pricing of Weather Derivatives including Meteorological Forecasts

Bachelorarbeit 2013 42 Seiten

BWL - Investition und Finanzierung



1. Abstract

2. Introduction

3. Overview Of Weather Derivatives

4. The Contract

5. Securities And Payoffs
5.1 Weather Options
5.2 Weather Swaps
5.3 Weather Futures And Forwards

6. Why Is The Market Still Illiquid?

7. Valuation Models Without Forecasts
7.1 Actuarial model
7.1.1 Burn Analysis
7.1.2 Index Modelling
7.1.3 Daily Modelling
7.2 Market-Based Approach
7.3 Arbitrage Pricing

8. Valuation Models With Forecasts
8.1 First Steps
8.2 Meteorological Forecasts And The Pricing Of Temperature Futures
8.2.1 The Model
8.2.2 The Data
8.2.3 Implementing the model
8.2.4 The Results
8.3 Simplified Temperature Model
8.3.1 The Model
8.3.2 Empiricai Data
8.3.3 Results
8.3.4 General Comments On Results

9. Conclusions

10. Bibliography

To my parents, who taught me how studying is an important, never-ending part of life and made many sacrifices in order to give me the possibility to live such a wonderful university experience.

“The Pricing of Weather Derivatives including Meteorological Forecasts."

1. Abstract

This paper analyses weather derivatives and the issue of pricing these financial instruments. The non-tradability of the underlying makes their pricing not straightforward and even if the Chicago Mercantile Exchange began trading the first weather contract in 1999, the market still witnesses very low volumes and is relatively illiquid. This theoretical analysis is focused on instruments whose underlying is temperature, since they are the most traded.

Due to the assumption of informational efficient markets, all available information should theoretically be included in the prices. However most existing models focus only on historical observations of temperature, actually excluding some relevant information.

The few models that have instead considered weather forecasts are analysed, and in particular the model introduced by Ritter, Musshoff, and Odening to price temperature monthly futures including weather forecasts is described in details. I've performed an analysis applying a simplified version of the model described, based on temperature data from Tampa, Florida, in 2007.

The results show that models with meteorological forecasts indeed outperform models that ignore them.

2. Introduction

The weather derivatives market needs a standard pricing model, with the necessary degree of accuracy and transparency. The large discrepancies between the currently available approaches are preventing the market from developing at a faster rate. Most of the available models fail to take into account weather forecasts in their valuation methods.

So, how to obtain a common valuation framework, capable of pricing weather derivatives including available meteorological forecasts?

The following sections try to answer this question.

A general overview of weather derivatives is done in the following section. Sections 4 and 5 present the elements of the weather derivative contract, the existing securities and their payoffs. In section 6 the reasons for the low trading volumes of such instruments are examined in more details and section 7 provides an analysis of the main kinds of valuation models that, however, do not deal with weather forecasts.

The models that do include meteorological predictions in their pricing process, and in particular the method introduced by Musshoff, Odening and Ritter (2011) for the calculation of theoretical prices of weather futures are investigated in section 8, in which a simplified version of the method is also implemented using data from Tampa, Florida in 2007.

The last section draws final conclusions and reflects on the potential for improvement

3. Overview Of Weather Derivatives

Weather derivatives are financial instruments that can be used by organizations or individuals as part of risk management strategy to reduce risk associated with adverse or unexpected weather conditions. They promise a payment to the holder based on the difference between an underlying weather index and a strike value.

Weather variability affects different entities in different ways. A ski resort would attract fewer skiers if there is little snow. An airline corporation can suffer long delays and huge losses due to stormy weather. Energy companies are strongly subject to weather variabilities: a natural gas supply company will sell less gas if winter is warmer than usual. Agricultural companies might suffer a drop in revenue due to below zero-temperatures or other abnormal weather conditions. These are just few examples of how weather conditions can affect profits and eventually lead to financial distress and bankruptcy.

In order to hedge against weather risk, companies can either acquire insurance coverage or buy/sell a number of weather derivative instruments. Weather derivatives differ from insurance contracts, since they do not require the owner to prove the damage occurred and allow a bigger range of events to be edged. Moreover, while insurance covers high-loss, low probability events (hurricanes, floods, earthquakes), the derivative contract deals with limited-loss, relatively high probability events.

Who transacted the first derivative is uncertain. Nevertheless, in July 1996, two American companies, Aquila Energy and Consolidated Edison, entered into a transaction that combined weather and energy risk. Weather derivatives slowly began trading over-the-counter in 1997 and, as the market began to expand, the Chicago Mercantile Exchange (CME) introduced the first degree-day futures and options in 1999.

In spite of the advantages over insurance, the volume of trade has been growing quite slowly since then.

But before turning to the reasons of the relatively low liquidity of the market, let's analyze first the typical elements of the weather derivative contract and the available securities.

4. The Contract

Weather derivatives can theoretically be designed for almost any weather variable, including temperature, rain, snow and wind. They can also deal with catastrophes, such as the hurricane contracts, which were introduced in March 2007, based on the CME Hurricane Index (CHI). The weather measure is quantified and an index is created.

So far the large majority of contracts has been constructed around temperature. Cumulative heating degree days and cumulative cooling degree days are the most common indexes.

A "Degree Day" is the measure of how much the daily average temperature deviates from a baseline indicator, usually 65 degrees Fahrenheit (or 18 degrees Celsius).

Days with temperatures below 65°F are called "Heating Degree Days", because these are days in which heating is more needed. When temperatures are instead above 65°F, people use air conditioners and therefore these days are called "Cooling Degree Days".

where Tt is the daily average temperature, defined as the average between daily maximum and minimum observed temperatures, reported by a certain weather station at day t "Cumulative degree days" are the sums of the daily HDDs or CDDs accumulated over a definite period of time, which is usually set as a month or a season.

where and are the beginning and end of the period dates.

Typically the HDD season includes months from November to March, while the CDD season is from May to September. April and October are usually called "shoulder months".

In order to define a weather contract, three other elements need to be introduced: the strike, the tick size and the limit.

-The reference or "strike" value (K) is the value of the underlying index at which the contract starts to produce returns for its holder.
-The tick size is defined as the payout amount attached to each unit change of the temperature index.
-The limit is the maximum financial payout (L) of the contract. If a limit is defined the derivative is said to be "capped".

The buyer of the contract can be also required to pay an upfront premium to the seller, depending to the type of security traded.

Contracts can be either traded on exchanges or over-the-counter.

Exchange-traded contracts are standardized products that are bought and sold by traders, largely through the Chicago Mercantile Exchange. The buyer’s account is debited or credited based on the fluctuating price of the weather risk covered in the contract.

Over-the-counter contracts are privately-negotiated products that are either warehoused or traded against other non-standardized products. OTC contracts offer greater flexibility compared to standardized products in terms of conditions, but they also bear the risk of default of the other party in the contract.

5. Securities And Payoffs

Once all the elements are clarified, let's see how the contract is financially settled using the weather index as the input of a payoff function.

Any function could theoretically be used, but in practice only few structures are applied. Swaps, call and put options are by far the most common. Since the underlying is a weather index, these types of derivative contracts are settled in cash.

For the scope of this work, only uncapped structures are considered. Empirically many options and swaps have maximum payoffs. However, the securities defined below can be considered good estimations, since the limits are usually set as rather extreme values.

5.1 Weather Options

Options can be call or put, and they are European contracts, meaning that they may be exercised only at the expiration date.

A call option is the contract which gives the holder the right to buy an asset by a certain date, for a predetermined price. (Hull,2005)

A put option gives the holder the right, but not the obligation to seN an asset by a certain date for a certain price. (Hull, 2005)

A premium is paid for the right of exercising the option.

The payoff to the buyer of a weather call option is:

A weather put option provides a payoff to the owner equal to:

A company who wants to protect itself against a loss due to a cold winter, will buy HDD calls and profit if temperature turns out to be above-normal.

A natural gas supply company who is concerned about a warm winter, will buy HDD put options and gain from below-normal temperatures.

Combinations of call and put options such as strangles, spreads and straddles can be implemented, the most famous being collars, in which a long call and a short put with different strikes are combined to hedge against high values of the underlying index.

5.2 Weather Swaps

Swaps are agreements between two parties to exchange cash flows in the future (Hull, 2005).

Payments are made between two parties, one side pays a fixed price, the other side pays a variable price.

In a standard, uncapped, swap the parties agree on a strike price. Most of the times, the weather swap has only one date in which cash flows are "swapped". If the temperature index accumulated during the period of the contract is larger than the strike, the seller pays the buyer an amount proportional to the difference between the two and vice versa.



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Titel: The Pricing of Weather Derivatives including Meteorological Forecasts