Weather Derivatives

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Weather Derivatives

• Dr Harvey Stern,
• Climate Manager, Victoria

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Introduction

• Evidence of the challenge faced by the
  meteorological community to become skilled in
  applying risk management products from financial
  markets is growing.
• An empirical approach to the pricing of weather
  derivatives is presented. The approach is
  illustrated with several examples.

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Background

• It is the energy and power industry that has, so
  far, taken best advantage of the opportunities
  presented by weather derivatives.
• Indeed, the first weather derivative contract was
  a temperature-related power swap transacted in
  August 1996.

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Weather Derivatives Defined

• Clewlow et al...(2000) describe weather
  derivatives as being similar "to conventional
  financial derivatives, the basic difference
  coming from the underlying variables that
  determine the pay-offs", such as temperature,
  precipitation, wind, heating degree days, and
  cooling degree days.

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Defining Cooling Degree Days

• Number of cooling degree days during a season is
  the accumulated number of degrees the daily mean
  temperature is above a base figure, usually 18
  deg C.
• Number of cooling degree days might be regarded
  as a measure of the requirement for cooling.

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Defining a CoolingDegree Day Call Option

• Strike 600 cooling degree days.
• Notional 100 per cooling degree day (above
  600).
• If, at the expiry of this contract, the
  accumulated number of cooling degree days is
  greater than 600, then the seller of the option
  pays the buyer 100 for each cooling degree day
  above 600.

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Pay-off Chart for the CoolingDegree Day Call
Option
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Pricing Approaches

• Historical simulation.
• Direct modeling of the underlying variables
  distribution.
• Indirect modeling of the underlying variables
  distribution (this involves simulating a sequence
  of data).

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Defining a 38 deg C Call Option(assuming a
temperature of at least38 deg C has been
forecast)

• Location Melbourne.
• Strike 38 deg C.
• Notional 100 per deg C (above 38 deg C).
• If, at the expiry of this contract (tomorrow),
  the maximum temperature is greater than 38 deg C,
  the seller of the option pays the buyer 100 for
  each 1 deg C above 38 deg C.

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Pay-off Chart for the38 deg C Call Option
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Determining the Price of the38 deg C Call Option

• Between 1960 and 2000, there were 114 forecasts
  of at least 38 deg C.
• The historical distribution of the outcomes are
  examined.

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Historical Distribution of Outcomes
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Evaluating the 38 deg C Call Option (Part 1)

• 1 case of 44 deg C yields (44-38)x1x100600
• 2 cases of 43 deg C yields (43-38)x2x1001000
• 6 cases of 42 deg C yields (42-38)x6x1002400
• 13 cases of 41 deg C yields (41-38)x13x1003900
• 15 cases of 40 deg C yields (40-38)x15x1003000
• 16 cases of 39 deg C yields (39-38)x16x1001600
• cont.

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Evaluating the 38 deg C Call Option (Part 2)

• The other 61 cases, associated with a temperature
  of 38 deg C or below, yield nothing.
• So, the total is 12500.
• This represents an average contribution of 110
  per case, which is the price of our option.

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Defining a Cooling Degree Day Put Option

• Strike 600 cooling degree days.
• Notional 100 per cooling degree day (below
  600).
• If, at the expiry of this contract, the
  accumulated number of cooling degree days is less
  than 600, then the seller of the option pays the
  buyer 100 for each cooling degree day below 600.

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Pay-off Chart for the Cooling Degree Day Put
Option
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A Forecast Error Put Option (defining error as
predicted minus observed)

• Strike 0 deg C.
• Notional 100 per degree of forecast error below
  0 deg C
• If the forecast underestimates the actual
  temperature, then the seller of the option pays
  the buyer 100 for each 1 deg C of
  underestimation.

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Evaluating theForecast Error Put Option

• Historical simulation yields a suggested price of
  67 for our put option.
• Two questions
• Does todays error influence the price?
• Does tomorrows expected weather pattern
  influence the price?

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Answering the First Question

• Todays error does influence the price
• If todays forecast is an underestimate, then
  tomorrows is also likely to be an underestimate,
  leading to a suggested option price of 75.
• If todays forecast is an overestimate, then
  tomorrows is also likely to be, leading to a
  suggested option price of 41.

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Answering the Second Question

• Tomorrows weather pattern does influence the
  price, for example
• If tomorrows weather pattern is moderate
  anticyclonic NNE, tomorrows forecast is likely
  to be an underestimate, leading to a price of
  77.
• However, if tomorrows weather pattern is strong
  anticyclonic NNE, tomorrows forecast is likely
  to be an overestimate, leading to a price of 47.

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A Monthly Rainfall Decile 4Put Option for Echuca

• Strike decile 4
• Notional 100 per decile below decile 4.
• If, at the expiry of this contract, the rainfall
  decile is less than 4, then the seller of the
  option pays the buyer 100 for each decile below
  4.
• Note Decile 1 is a rainfall total in the lowest
  10 of historical records, decile 2 is in the
  second lowest, decile 3 is in the third lowest,
  etc.

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Pay-off chart for the Monthly Rainfall Decile 4
Put Option
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Historical Distribution of Outcomes (for cases
when the Southern Oscillation Index is in the
lowest 3 deciles - an indicator of dry conditions)
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Evaluating the Decile 4 Put Option(for cases
when the Southern Oscillation Index is in the
lowest 3 deciles)

• 9 cases of Decile 1 yields (4-1)x9x1002700
• 6 cases of Decile 2 yields (4-2)x6x1001200
• 4 cases of Decile 3 yields (4-3)x4x100400
• The other 25 cases (Decile 4 or above) yield
  nothing.
• leading to a total of 4300, and an average
  contribution of 98, which is the price of our
  put option.

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Evaluating Other Derivatives

• An experiment is conducted to illustrate the
  importance of mean reversion and jumps in the
  evaluation of other financial derivatives.
• Mean reversion and jumps are features of the
  Monte Carlo approach to modeling weather
  derivatives.

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The Experiment

• It is assumed that stocks are purchased following
  a break in an extended sequence of consecutive
  price falls.
• It is assumed that stocks are short-sold
  following a break in an extended sequence of
  consecutive price rises.
• Net returns are determined.

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Mean Reversion

• Mean reversion is demonstrated by
• The average return being 4.51 with a standard
  deviation of 12.15 yielding the result-
• The average is different from zero at the 0.1
  level of significance, the ve return reflecting
  the operation of mean reversion.

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Jumps

• The operation of jumps is illustrated in the next
  slide, which presents the ratio
• (frequency of returns from experiment)
• (frequency of returns if distribution normal)
• that ratio being presented in half standard
  deviation steps from the mean.

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The Ratio(note the much higher frequency of
extreme returns)
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The ratio(without the extreme cases)
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Concluding Remarks

• An empirical approach to the pricing of weather
  derivatives has been presented.
• The approach utilises a range of data types to
  price weather derivatives, including forecast
  accuracy data.
• It has been shown that mean reversion and jumps,
  features of the Monte Carlo approach to the
  modeling of weather derivatives, should also be
  included in the modeling of other derivatives.

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