Meteorological Insurance and its Derivatives Pricing and Risk Management in the Context of Big Data *

Transcription

1 Scienific Journal of Informaion Engineering May 017, Volume 7, Issue 1, PP.7-33 Meeorological Insurance and is Derivaives Pricing and Risk Managemen in he Conex of Big Daa * Na Niu 1, Yongmin Quan 1, Hongyi Li 1, Zhezhi Jin 1 1. College of Science, Yanbian Universiy, Yanji 13300, China jinzhezhi@sina.com Absrac As legal inegraion of marke and he revializaion of meeorological indusry, we can esimae he demand for meeorological marke more and more, herefore proposed o formulae a reasonable price of weaher insurance and is derivaives and risk valuaion mehod is paricularly imporan. Based on he response o climae warming rend and he connecions beween regional new mulivariae probabiliy model of he emperaure, combusion mehod and he Mone-Carlo simulaions was used o (CDD/)-cooling, heaing, index opions for accurae pricing. Through muliple emperaure probabiliy model o pricing of weaher derivaives, and o hedge he risk meeorological insurance producs, using he CDD/ index opions o reasonable weaher insurance risk aversion, and presen a good effec on risk managemen. Keywords: Mulivariae Temperaure Model; Weaher Insurance; Opion Pricing; Risk Managemen 1 INTRODUCTION In order o promoe he applicaion of financial derivaives pricing and mulivariae probabiliy model of emperaure, reflecs he climae warming rend and before each new mulivariae correlaion beween regional emperaure probabiliy model[1-], using he CDD/ index opions o reasonable risk aversion of weaher insurance, by agreemen price as a benchmark for Beijing CDD pu opion o hedge of opimizaion, he comparison before and afer using hedging loss disribuion, analyze he risk of loss disribuion dispersion effec on he effecs of lower premiums, i is concluded ha he weaher derivaives can be very good hedging effec of weaher insurance. METEOROLOGICAL INSURANCE PRICING Temperaure probabiliy model based on mulivariae ime series model, revised he ime series regression models can be variable uni emperaure probabiliy model, a he same ime improve he Cao Wei model[3], because he model a a ime only for a regional modeling analysis, and o a number of differen regional econic emperaure model could no be achieved, here are limiaions. On he basis of his model, he auhor pus forward a new model before, added each regional virual variable as he analysis of he facors o esablish model, increase he represenaion in differen regions of he variables and ineracion variables (variables can reflec boh he domain RM r m, d and he effec of he daily value ) in order o be able o reflec he differen regions of he emperaure effec. So he mulivariae ime series model specific expressions are as follows: Y X X X R R R X r, yr, 0 1 1, 1, , , R X R X R X T RT R T , , , r, yr, (1) * Fund suppor:by he Jilin Provincial Deparmen of Educaion, "Thireen Five" scienific and echnological research projecs o suppor funding (Kyrgyzsan each he word [016] No. 48) - 7 -

2 1, r r ( 0 Seoul), r ( 1 Taegu), r ( Kwangju), r ( 3 Inchon), R r 4 Busan r 5 Mokpo r 6 Beijing r 7 Wuhan r ( ), ( ), ( ), ( ), R r, Rr r ( 8 Chongqing), r ( 9 Tianjin), r 10 ( Shanghai), r 11 ( Guangzhou) 0, In he formula, he Y, X, T respecively represen he afer sandardizaion of he average emperaure, he virual variables and he oal rend. The mulivariae model can' made i clear ha he relaionship beween geographical. Using he mulivariae ime series model, VAR1 models he residuals and esimaes he correlaion and auocorrelaion beween differen regions, and esablishes a model ha can show he srucure of residuals. s s 1 As, s yr , yr, s T 1, yr, 11 T T 1, yr, r,1,1 r,1, r,30,366 1,1 1,1 1,1 1,1 1 1, () As i. i. d MVN 01 1, (4) 11 In previous sudies, using he pricing mehod is adoped o predic he fuure of all of he emperaure scene spending premium plus he average amoun of he safey value of gross premium calculaion, which generaed by Mone-Carlo simulaion for he number of days each scenario is lower han he reference emperaure calculaed separaely according o he region, he average days more han 35 days as pure insurance cos. Given he huge losses may be produced in he fuure, se more han days 1 imes he sandard deviaion o he safey value o calculae he gross premium, able 1 by mulivariae probabiliy model o calculae he emperaure of each regional premium. Compared wih Changsoo Lee model [4], securiy value-added par of he premiums decreased a lo, by mulivariae probabiliy model can calculae he emperaure are lower han hose of exising insurance premium. TABLE 1 INSURANCE PREMIUM CALCULATED BY THE SIMULATION EXPERIMENT Region Average Sandard Deviaion Gross Premium Seoul Taegu Kwangju Inchon Busan Mokpo Beijing Wuhan Chongqing Tianjin Shanghai Guangzhou METEOROLOGICAL DERIVATIVES (CDD/) PRICING The weaher derivaives were originally impored in 1999 by he Chicago Mercanile Exchange (CME).In 008, a oal of 35 ciies, mainly he Unied Saes and Japan, carried ou on he emperaure index of commodiy ransacions. Among hem, Japan, for example, he scale of weaher derivaives increased by a full en imes from 000 o 005.A presen, weaher derivaives are sill a relaively new hing for Chinese people. Boh in he heoreical and physical (3)

3 circles, here is no a lo of aenion o i, and he relaed lieraure is very lile. Currenly, he only available research is based on qualiaive aspecs of inroducory analysis. I does no pu he research of weaher derivaives ino China's specific economic and social environmen, and lacks he pracical applicaion effec, and i lacks professional research on he pricing of weaher derivaives. The opions sudied in his paper are mainly are mainly focus on he OTC opions used by enerprises o hedge he risk of emperaure. Such OTC opions are mosly for summer(may-sepember) and winer(november-march) emperaure. I is a long erm opion wih a mauriy of 6 monhs or more. The value of he opion is no only relaed o he emperaure a mauriy bu also o he pah-dependen opion affeced by he emperaure change in a cerain ime. In his case, we price he CDD/ index opions a T 1 o T in he fuure [5-6]. Firs, he formula of he CDD and he index for he fuure ime T 1 o he ime T is: T (T 1,T ) max 18 Y,0 T1 T CDD(T 1,T ) max Y 18,0 T1 Using he index of he above definiion, he formula for calculaing he opion price is: 1 C, T, T, K e 1 rt E max T, T K,0 P, T, T, K e 1 r T 1 E max K T, T,0 In he formula, is ime, and K is he execuion price of he opion, and r is he risk-free rae. Through he above formula, we can ge he price of he opion a any ime of he ineres rae r. In he case of he risk neural probabiliy, he risk-free rae can be approximaed. Similarly, for he call opions and pu opions of CDD, he price calculaion formula is: 1 C, T, T, X e 1 rt E max CDD T, T K,0 P, T, T, X e CDD 1 rt 1 E max K CDD T, T,0 I is very difficul o find he analyic soluion according o he formula of he opion pricing. Compared wih he parameers which affec he price of he opion, given he characerisics of he pah dependen opion, he price of he simulaed emperaure opion is deermined. Take he Beijing Area as an example. Table shows he acual value of /CDD in Beijing from 1981 o 010. Figure 1 shows he CDD / index calculaed using he CDD / index opion pricing mehod. I can be seen ha he CDD index increases gradually wih he increase of he year, while he index shows he rend of decreasing wih he increase of he years. The rend is due o he gradual warming of he global climae, which leads o an annual increase in he average annual emperaure, resuling in a year-on-year increase in he CDD index and a decrease in he index year by year. TABLE ACTUAL VALUES OF CDD/ OF BEIJING IN THE PAST YEAR Period (Year) Saisic Average Sandard Deviaion CDD Beijing (5) (6) (7) (8) (9) - 9 -

4 FIG.1 CDD/ INDEX Mone-Carlo simulaion experimen opion pricing, which is achieved by simulaing he underlying asse price. In he simulaion of emperaure change, he seasonal variaion of emperaure, he mean response of he mean emperaure and he emperaure change of he geographical locaion are aken ino accoun. The Mone-Carlo mehod and he saisical characerisics of emperaure o simulae a large number of random numbers and weaher condiions, and is flexible in pricing various weaher derivaives in differen regions. On he basis of perfecing he mulivariae emperaure probabiliy model and he Cao-Wei model [7], he improvemen of he calculaion accuracy mainly refers o he average, sandard deviaion based on he calculaion of CDD/ index, while increasing he uiliy of Mone Carlo simulaion mehod in opion pricing. Table 3 is he resul of he CDD/ index simulaion experimen in Beijing. In he following able, we can clearly see he difference beween he mulivariae emperaure probabiliy model and he Cao-Wei model afer inroducing he rend of climae warming. I can be seen ha he deviaion of he probabiliy model of he muliple air emperaure is smaller han ha of he Cao-Wei model. Compared wih he probabiliy of real value of he model and agreemen price in Beijing, he corresponding price can be calculaed by wo models when he agreemen price is shown in he following able. Region Beijing TALBLE 3 CDD/ INDEX STATISTICS BASED ON MONTE-CARLO SIMULATION Parameer CDD Mulivariae Model Cao-Wei Model Mulivariae Model Cao-Wei Model Average Sandard The difference beween he wo models can be clearly seen hrough he char. The call opion is a siuaion where he underlying asse price is higher han he price of he conrac, and he pu opion refers o he siuaion where he underlying asse price is lower han he conrac price. Table 4 and Table 5 are he probabiliies of he CDD/ in he money opion based on he mulivariae emperaure probabiliy model. And figure is he resul of he CDD/ index disribuion. TABLE 4 COMPARISION OF CDD IN THE MONEY OPTION Execuion Price CDD Call Opion CDD Pu Opion Mulivariae Model Cao-Wei Model Mulivariae Model Cao-Wei Model TABLE 5 COMPARISION OF IN THE MONEY OPTION Execuion Price Call Opion Pu Opion Mulivariae Model Cao-Wei Model Mulivariae Model Cao-Wei Model

5 FIG. CDD/ INDEX DISTRIBUTION (BEIJING) The mulivariae emperaure probabiliy model is suiable for he model of daily emperaure change, he rend of climae change, and he relaionship beween differen regions. Based on his model, he Mone Carlo simulaion mehod is used o accuraely pricing CDD / index opions. In he daa below, i can be shown ha he model is basically he same as he oher models, bu he value of CDD/ index opion is valid and reasonable [7-8]. The model is closer o he fac ha he resuls in accurae pricing opions and he developmen of appropriae emperaure weaher derivaives plays a very imporan role, i has very high pracical value of opion pricing, for he use of CDD/ index opion reasonable hedge agains weaher insurance risk managemen play a very good effec. 4 RISK MANAGEMENT TABLE 6 CDD INDEX OPTION PRICING Negoiaed Price CDD Call Opion Pu Opion TABLE 7 INDEX OPTION PRICING Negoiaed Price Call Opion Pu Opion The weaher derivaive is a financial insrumen used o circumven he weaher risk, is refers o he change of fuure climae change caused by he uncerain economic uni revenue uncerainy. Weaher derivaives is a kind of derivaives, he fronier of he rend of globalizaion along wih he developmen of he marke, began o appear in he world especially developed very fas in Europe and he Unied Saes sock marke rading volume: Weaher derivaives rading volume and he rading varieies increased rapidly, and he geographical scope of rade expanded rapidly, also increase he source of suppliers and buyers. Vas in our counry, he weaher changes in he differences beween differen Regions. Because our counry belongs o he monsoon climae, he emperaure and precipiaion and oher major indicaors of he magniude of he larger changes in he weaher change uncerainy is higher, he degree of deviaion from normal condiion, abnormal weaher occurrence probabiliy is higher, herefore our counry here is a huge demand for weaher derivaives and risk managemen [9-1]. Through he muliple emperaure probabiliy model, Based on agreemen price opimizaion for he Beijing CDD pu opions are obained. As a resul of risk hedge under he condiion of each regional sales differen, o make a sudy of changes in regional risk porfolio loss disribuion, loss disribuion characerisics change wih risk hedging. In Beijing ciy as well as he sample by using a combinaion of risk hedging loss disribuions are compared, and analysis he effec of he loss disribuion of he risk diversificaion effec brough abou lower premiums. The risk managemen of how o use weaher derivaives is carried ou in deph, especially on he hedging effec of weaher risk

6 4.1 The Opimal Risk Hedging of Beijing CDD Pu Opion is based on he Agreemen Price By mulivariae emperaure probabiliy model simulaion o deal he price as a benchmark for Beijing CDD pu opion hedging of opimizaion, according o he correlaion coefficien as well as he opion price of he opimal hedge conrac number and he hedging cos, as shown in able 8. TABLE 8 OPTIMAL RISK HEDGE FOR THE BEIJING CDD PUT OPTION BASED ON THE AGREED PRICE Agreemen Price Opimized Correlaion Hedging Conac Coefficien( ) * Number( H ) Opion Price Hedging Coss *Simulaion resuls using mulivariae emperaure probabiliy models 4. Changes in he Disribuion Characerisics of he Risk of Hedge Losses Price of differen proocols, he average loss is he same, are all 85.86%, bu losses is lile differen from sandard deviaion and loss probabiliy. When he price of he agreemen is 960, he sandard deviaion is 80.77, and he loss probabiliy is I can be seen ha compared wih oher agreemen prices, he sandard deviaion and loss probabiliy of he agreemen a 960 is he smalles. Using compuer simulaion of loss disribuion characerisics, can clearly see ha risk hedge differen proocol prices afer he loss of he corresponding sandard deviaion and he change rend of loss probabiliy, risk hedging losses afer he sandard deviaion of changes is o reduce as agreemen prices rise rapidly, agreemen reached 960 here was a low price, and hen gradually increased wih he increase of price agreemen, bu increased gradually slow down. Probabiliy of hedging losses afer he change is presened as agreemen prices rise rapidly reduced, agreemen reached 960 here was he lowes price, and hen rise rapidly and gradually slow rise rend,as he following able 9. TABLE 9 VARIATION IN LOSS DISTRIBUTION CHARACTERISTICS AFTER ADOPTING RISK HEDGING Agreemen Price Loss of Balance Sandard Deviaion of Loss Probabiliy of Loss Comparison of Risk Disribuion afer Risk Hedging for he Beijing Region The risk of hedging of CDD pu opion wih 960 agreemen price in Beijing is obained, and he corresponding loss average, loss sandard deviaion and loss probabiliy before and afer risk hedging are obained, and he value afer risk hedging is obviously reduced. As shown in Table 10. The pos-hedge loss has been significanly reduced, and he risk disribuion before and afer he risk hedging is shown in Figure 3. Afer hedging, he sandard deviaion is reduced by abou 8.6% and he probabiliy of loss is reduced by abou 31.8%. This means ha risk hedging can be used o manage risk well, reduce losses and increase revenue. TABLE 10 COMPARISION OF RISK DISTRIBUTION BEFORE RISK HEDGING Sage Loss of Average Sandard Deviaion of Loss Probabiliy of Loss Before Risk Hedging Afer Risk Hedging

7 5 CONCLUSIONS FIG. 3 THE DISTRIBUTION OF LOSSES BEFORE AND AFTER HEDGING Firsly, in assessing he pricing of weaher insurance producs, aking ino accoun he impac of climae warming rends, if he emperaure model can no reflec his phenomenon, hen he cos of weaher insurance can be inferred. Secondly, i is possible o improve he adapabiliy of he model by using he muliple emperaure probabilisic model approximaion o improve he fiing degree and versailiy of he model o comprehensively evaluae and manage he meeorological insurance risks of each region. In addiion o improving he adapabiliy of he model can be used as a way o reduce he excessive insurance coss o a suiable level of a program. Finally, i is proved ha he geographical combinaion in meeorological insurance can significanly improve he risk dispersion effec, which is an imporan reason o reduce he cos of weaher insurance by improving he price of he model by improving he suiabiliy of he model, and i is also an imporan reason for reducing he cos of weaher insurance. REFERENCES [1] Zhezhi Jin, Pricing and risk evaluaion of weaher insurance based on mulivariae emperaure model[j].journal of Yanbian Universiy:Naural Science,01,38(3): [] Zhezhi Jin, Lianxin Wei, Jizhe Cui, PRICING Mehod for Weaher Opions Based on Mulivariae Temperaure Model[J].Universiy of Shanghai for Science and Technology,015,37(3):0-4. [3] Cao, M, and J. Wei. Pricing he weaher [J].Risk,000, [4] Changsoo Lee, Sudy on he pricing of meeorological insurance based on he emperaure probabiliy model[j]. Insurance developmen research, 008,19(): [5] Lee J H.A sudy on he valuaion of he CDD/ weaher opions[j].the Journal of Korean Securiies Associaion, 00,31: [6] Zheng Hu, Qingma Dong, Weaher risk managemen and is laes research progress[j]. Theoreical discussion, 01(370): [7] Cao, M, and J. Wei. Weaher Derivaives Valuaion and Marke Price of Weaher Risk [J]. The Journal of Fuures Markes, 004, 4(11): [8] Guoguang Liu, Research on pricing of weaher forecasing and weaher derivaives[j]. Forecas, 006(6):8-33. [9] Zheng Wang, Research on weaher opion pricing based on emperaure index[j]. Commercial Economy, 01():8-30. [10] AK Alexandridis, AD Zapranis. Weaher derivaives: Modeling and pricing weaher-relaed risk[j].case Hu,013. [11] HH Huang,YM Shiu,PS Lin. and CDD opion pricing wih marke price of weaher risk for Taiwan[J].Journal of Fuures Markes,008,8(8): [1] Dischel B.A model for weaher risk [J].Energy and Power Risk Managemen, 1999, 11(3):0-1. AUTHORS 1 Na Niu (1993-),Maser graduae, research direcion: applicaion saisics @qq.com. Zhezhi Jin(1977-),lecurer, graduae uor, research direcion: informaion saisics and insurance acuarial. Now, he is a professor in he mahemaics, Yanbian Universiy