Pricing Exchange Options And Extremum Options With Tree Lattice Method

Option is a contract signed by the seller and the buyer, this contract gives the holdera right to buy or sell an asset with a determined strike price in the future date, instead ofan obligation of carrying out the contract. Option pricing is an important research field infinancial theory and practice.In 1973, Black and Scholes, as the pioneers, established the option pricing formula.Since then, the option market has been developing rapidly. People have regarded Black-Scholes'option pricing theory as the classic financial analysis technology, made promotions,and achieved fruitfully. Generally speaking, option pricing methods can be divided into an-alytical methods and numerical methods, the former of which can get the option's analyticalprice( that is known as the explicit solution )by applying Mathematical analysis means, prob-abilistic methods, and so on; the latter of which are often taken when it is difficult to obtainthe price formula during the process of option pricing, and they include Monte Carlo simu-lation method, tree lattice method, finite difference method and so on. With the developmentand wide application of computer technology, people like to use numerical methods to priceoptions, especially for those new options who have complex profit structure.Throughout the pricing research of one asset option, the binomial tree method, trino-mial tree approach, and pure Monte Carlo simulation method have played an important roleand also have been improved. However, in the pricing process of multi-asset option, the re-search literatures which use tree lattice method and Monte Carlo simulation method are rare.This is because an option contract in practical market is often subject to prices'changes ofseveral underlying basic products, not the individual asset price. Therefore, the study ofthe multi-asset option pricing model has an important theoretical value and practical signif-icance, however, the option pricing of multi-asset model is far more complicated than thatof one-asset model, and difficult to get option's explicit price. In this paper, we mainly ap-ply tree lattice method, combine with Monte Carlo simulation to discuss option pricing ofmulti-asset model, focus on the pricing of two options—Exchange Options and ExtremumOptions, and then propose major work and conclusions:The first chapter describes the necessity and significance of research in option pricing, states research situation on tree lattice method and other numerical methods, Exchange Op-tions and Extremum Options at home and abroad, and then proposes this paper's source andmajor research contents.Chapter II introduces the tree lattice approach and its application in option pricing.Chapter III makes use of tree lattice method and Monte Carlo method to calculate pricesof Exchange Options which pay dividends, and then compares with explicit pricing of theBlack-Scholes option model.Chapter IV uses tree lattice method and Monte Carlo method to valuate prices of Ex-tremum Options which pay dividends, and then compares with the explicit pricing.In chapter V, we summarize the content of this paper, and put forward the work prospectsfor further research in the related subject.