Recombining Binomial Tree Method For Pricing Options With Discrete Dividend Payments

It is challenging to price options on stocks with known discrete dollar dividends.Although many excellent theoretical models have emerged,there is no perfect model that can solve the problem of cash dividend option pricing.In addition,when the underlying asset pays dividends,the binary tree with overlapping nodes no longer overlaps,and the phenomenon of node explosion is easy to occur.For this,we proposes a novel yet simple method for constructing a recombining binomial tree via balanced dividend adjustments（BEF）.The driver behind the motivation is obvious that Spot and Forward Models overall underprice and overprice options,respectively.The very point of our approach lies in the deduced weights which are both intuitively clear and mathematically correct.With this proposed model,the mixed adjustment（closed-form）formula is attained for pricing European option with discrete dividends regardless of a single dividend payment or multiple dividends.Next,we choose to use the binary tree with non-coincident nodes as the comparison benchmark to strictly prove the accuracy of the binary tree method with node coincidence proposed in this thesis for European options from a mathematical perspective.In addition,heuristically proved that for American option pricing,the binary tree method with node coincidence is an excellent approximation of the binary tree method with node non-coincidence.Finally,we also proved the correctness of the above conclusions through in-depth numerical experiments.For European options,all the pricing errors of our proposed new node coincidence pricing method do not exceed 0.5%.In this thesis,a total of 57 options are carried out in numerical experiments.Among them,38options have an absolute value of less than 0.50%.Compared with those models/methods that have been proposed so far,this novel approach（BEF）has several appealing features.First,this BEF Model can offer a real closed-form pricing formula like the classical B-S formula,therefore the calculation for option pricing is immediate rather than time-consuming.Second,it is general and applicable for both single and multiple discrete dividends cases.Third,our approach is logically and conceptually appealing since it is intuitively clear and mathematically ensured.Furthermore,it is amazingly accurate.Finally,the research question in this article comes from the classic book written by Hull^[15].It is verified by theoretical proof and numerical experiment that the BEF model is better than the spot and forward models in numerical pricing errors,which enriches the dividend payment option pricing theory and has certain reference significance.