Theoretical Study And Empirical Analysis Of Option Pricing Model In Imperfect Market

The derivatives market has developed rapidly in the past forty years.Option contracts,as a financial product with the highest degree of derivation,which take hedging,risk aversion and speculative profits into account,have experienced unprecedented rapid development.This rapid development process cannot be achieved without the promotion of B-S-M pricing formula.Compared with the mature development of overseas option markets for decades,domestic option market is still in its infancy.The option market still has the unbalanced and insufficient development.Just because the option market is indispensable to the speedy,steady and prosperous development of a nation's financial condition.It is particularly important to find a set of pricing theory and risk control method suitable for China's own options.In this paper,we first give the derivation process of B-S-M pricing formula.Compared with the original literature,which gives the pricing formula by solving the partial differential equation,we consider the equivalent martingale measure method and give the derivation process of B-S-M pricing formula under the condition of risk neutrality.Faced with the current situation that the over-the-counter non-standard options,i.e.singular options,are mainly traded in the option market,we briefly introduce several main singular options.And because their structures are more complex than standard options,it is more difficult to get their pricing formulas.Although the B-S-M pricing model is derived under the standard European option environment,the derivatives pricing idea contained in this model can be widely used in most innovative products different from standard options in the nowadays option market.On the basis of our predecessors,we give the analytic pricing formulas of common singular options.The B-S-M option pricing formula can only be established under the complete market conditions,Many assumptions do not satisfy the actual market conditions,such as assuming the expected return ? and volatility of the underlying stock ?are constants.Therefore,how to price options under imperfect market conditions then seems important to us.In this paper,we introduce the concept of non-linear expectation to consider the Choquet upper and lower prices and the minimax price of option in incomplete market.With the help of g-expectation defined by backward stochastic differential equation,we give the explicit pricing of standard European option contracts under these conditions.Here,we define a "fuzzy coefficient" k to reflect the degree of uncertainty in the market.Secondly,we make an empirical analysis of the maximum price pricing model in incomplete market.Taking a 50ETF call option in Shanghai Stock Exchange as a sample,we calculate the optimal parameter value k through the programming,so that the predicted price obtained by the above pricing model is closest to the real market price,then apply this parameter value to the option outside the sample,considering the predicted price and the actual price of other call option contracts,the degree of difference and the reasons are analyzed accordingly.At the same time,a more in-depth discussion of the model is made,and the differences in the empirical process are summarized,the reasons are analyzed,and the improvement methods are given.Finally,we summarize and prospect this paper.It should be noted that in imperfect market environment,only the Choquet upper and lower prices of standard European options can be calculated by the minimax prices.The maturity return function of such option contracts is a monotonic function of the maturity price of underlying assets.For those various of singular options in today's option trading market,since they are path-dependent,the maturity return function is not a monotonic function of the maturity price of underlying assets anymore.So how to calculate their Choquet upper and lower prices in incomplete market is a feasible development direction of option pricing theory in the future.