Study Of The Weather Derivatives Pricing Problems

With people's more and more knowledge to weather risk, especially the El Nino appeared in1997, many companies have to explore the market of weather risk and weather derivative. With thecorresponding, the pricing theory of weather derivative is becoming more mature and perfect in theprosperity of the market. Though the classical B-S model has given the popular pricing formulaas to the ordinary derivative, weather derivative is usually traded outside the market, the materialcontent of the contract may be decided by the both sides wish and it has more ?exible standard.So the pricing of weather derivative is restricted by various assuming conditions. In this paper,based on the B-S model such as existing interest risks, stochastic volatility and weather indexwith discontinuous jump, we try to build the pricing model of several certain weather derivativescontract and by using the method of PDE, the closed form solution of the model is obtained.Weather options are the core tool of risk management. It can help us to avoid weather risk andprovide the more profit chance to investor and so it is welcome to the public. With first appeared inNorth America in 1997, weather option pricing theory has developed quickly and they become thesignificant component of modern finance theory. In this paper, we first introduce the emergence,the problems we will study, development and actuality of options pricing theory.Cumulate growing degree day options which are important part of weather option mainlyused to help the cropper operator to deal with the poor weather, avoid risks and lock the profit.As to the cropper with growth index usually has many growing stages in its growing process andevery growing stage needs a certain quantity of heat to turn into the next growing stage insteadof reduction or zero foison, in order to maintain both profits of the option holders, there must beobstacle items and resetting items in the option. In Chapter 2, we established the multi-obstaclemodel and compounding (obstacle, resetting) model according to the cumulate growing degreeday options. By calculating it stage by stage and using the method of PDE, the obvious pricingformula is obtained.In Chapter 3, the problem comes from the outer performance hot degree day options. Outerperformance hot degree day options are contracts based on the difference in temperature betweentwo places and its traded result is the holder compensates when the difference value changed intopayoff area. This option mainly applied to the energy sources industries such as natural gas, oiland firedamp. Assuming the market interest rate obey the Vasicek model, the paper transferredthe three-dimensional pricing problem to two-dimensional PDE pricing problem by transformingthe pricing nuits under the B-S model frame then using PDE mothed to get the analytic solution.In actual situation, weather index usually jumps at different degree in the period of validity and the waving rate varied randomly. In Chapter 4, we study the reset Cumulate growing degreeday options when the volatility obeys the Heston model and straddle cumulate growing degree dayoptions when weather index action obeys the jump-diffusion model. The corresponding pricingmodel and pricing formula are also given in Chapter 4.Lastly, a summary of this paper is made and further research directions are put forward.