Modelling of Temperature Dynamics for Weather Derivatives Pricing - - PowerPoint PPT Presentation

Modelling of Temperature Dynamics for Weather Derivatives Pricing Emmanuel Evarest Sinkwembe

Department of Mathematics, University of Dar es Salaam Department of Mathematics, Link¨

• ping University

First Network Meeting for Sida- and ISP-funded PhD Students in Mathematics Stockholm 7–8 March 2017

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My Advisors

Martin Singull Fredrik Berntsson Xiangfeng Yang Wilson Charles

Main advisor Assistant advisor Assistant advisor Assistant advisor Link¨

• ping University

Link¨

• ping University

Link¨

• ping University

UDSM

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Research Focus

In this project, we are trying to formulate a model that captures most of the features of temperature dynamics, and then use the model to price weather derivatives written on temperature indices. Definition Weather derivative is a financial instrument whose payoff is dependent on weather variable measured at specific weather station on given period of time. Weather variables are indexed in order to make them tradable like

• ther index products such as stoke index.

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Temperature Indices

Given DAT Td(t), reference temperature Tref and contract period

• f N days

Indices Definition accumulated indices HDD max{0, Tref − Td(t)}

N

• t=1

max{0, Tref − Td(t)} CDD max{0, Td(t) − Tref }

N

• t=1

max{0, Td(t) − Tref } CAT

N

• t=1

Td(t) PRIM

1 N N

• t=1

Td(t)

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Temperature dynamics

The dynamics of daily average temperature Td(t) is defined by Td(t) = ˜ Td(t) + Sd(t) (1) where ˜ Td(t) and Sd(t) are deseasonalized temperature values and seasonality components respectively.

Time(days)

1000 2000 3000 4000 5000 6000

Temperature[° C]

• 25
• 20
• 15
• 10
• 5

5 10 15 20 25

Time(days)

1000 2000 3000 4000 5000 6000

Deseasonalized Temperature

• 25
• 20
• 15
• 10
• 5

5 10 15

Figure: Td(t) for Malmsl¨ att superposed with Sd(t) (left) and ˜ Td(t) (right)

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Temperature dynamics continued...

The seasonal component is defined by Sd(t) = A1 sin 2π 365(t − A2)

• + A3t + A4,

(2) where A1 is the amplitude, A2 is the phase angle, A3 and A4 are coefficients for linear trend. The deseasonalized temperature is given by ˜ Td(t) = ˜ Tt,1 : d ˜ Tt,1 = (µ1 − β ˜ Tt,1)dt + σ1 ˜ Tt,1dWt, ˜ Tt,2 : d ˜ Tt,2 = µ2dt + σ2dWt. (3) The pricing of WD contracts based temperature indices is carried

• ut under the equivalent measure.

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Impact and Applications of My Research

Meteorology sector, Insurance and re-insurance companies, energy industry Contribution to teaching staff and research at UDSM, Contribution of knowledge in the field of derivatives pricing for non tradable underlying variables.

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Tack s˚ a mycket! Thank you!

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