Modelling of Temperature Dynamics for Weather Derivatives Pricing Emmanuel Evarest Sinkwembe Department of Mathematics, University of Dar es Salaam Department of Mathematics, Link¨ oping University First Network Meeting for Sida- and ISP-funded PhD Students in Mathematics Stockholm 7–8 March 2017 1 / 8
My Advisors Martin Singull Fredrik Berntsson Xiangfeng Yang Wilson Charles Main advisor Assistant advisor Assistant advisor Assistant advisor Link¨ oping University Link¨ oping University Link¨ oping University UDSM 2 / 8
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 other index products such as stoke index. 3 / 8
Temperature Indices Given DAT T d ( t ), reference temperature T ref and contract period of N days Indices Definition accumulated indices N � HDD max { 0 , T ref − T d ( t ) } max { 0 , T ref − T d ( t ) } t =1 N CDD max { 0 , T d ( t ) − T ref } � max { 0 , T d ( t ) − T ref } t =1 N CAT � T d ( t ) t =1 N 1 � PRIM T d ( t ) N t =1 4 / 8
Temperature dynamics The dynamics of daily average temperature T d ( t ) is defined by T d ( t ) = ˜ T d ( t ) + S d ( t ) (1) where ˜ T d ( t ) and S d ( t ) are deseasonalized temperature values and seasonality components respectively. 25 15 20 10 15 Deseasonalized Temperature 5 10 Temperature[° C] 0 5 0 -5 -5 -10 -10 -15 -15 -20 -20 -25 -25 0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000 Time(days) Time(days) att superposed with S d ( t ) (left) and ˜ Figure: T d ( t ) for Malmsl¨ T d ( t ) (right) 5 / 8
Temperature dynamics continued... The seasonal component is defined by � 2 π � S d ( t ) = A 1 sin 365( t − A 2 ) + A 3 t + A 4 , (2) where A 1 is the amplitude, A 2 is the phase angle, A 3 and A 4 are coefficients for linear trend. The deseasonalized temperature is given by � ˜ T t , 1 : d ˜ T t , 1 = ( µ 1 − β ˜ T t , 1 ) dt + σ 1 ˜ T t , 1 dW t , ˜ T d ( t ) = (3) T t , 2 : d ˜ ˜ T t , 2 = µ 2 dt + σ 2 dW t . The pricing of WD contracts based temperature indices is carried out under the equivalent measure. 6 / 8
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. 7 / 8
Tack s˚ a mycket! Thank you! 8 / 8
Recommend
More recommend
