Approximate Price Formulas For B-S-M Model,SVI Model SABR Model And Error Test

In the past half century,the derivatives market has developed rapidly,and the theory of option pricing has also developed rapidly.The methodology for studying option pricing issues is also constantly evolving.General equilibrium pricing model and arbitrage equilibrium pricing model have been applied to option pricing problems successively.When the role of arbitrage is limited,some option pricing theories focus on starting from the market,using models to describe the laws of the market,and using the laws to guide the investment process.In 1973,the B-S-M model solved the problems that have plagued the academic circles for many years and established a complete analysis framework for option pricing.In the following period,many scholars have continuously relaxed their assumptions on the basis of the B-S-M model,and put forward many option pricing models that have theoretical foundations and are highly practical.The more representative ones are the local volatility model,SVI model,SABR model,etc.Option pricing models are mostly based on stochastic models.Learning models require a certain theoretical basis,and there are certain thresholds for ordinary investors who have not received higher education.Institutional investors such as market makers standardize the options market,but the development and growth of the options market requires the participation of ordinary investors.In order to lower the threshold for participating in option trading,this paper selected the more representative B-S-M model,SVI model,and SABR model,summarized their common features,proposed the price approximation formulas of the three models,and empirically tested the approximate formula calculation results the error from the original model and the error from the actual option data.This article first derives the B-S-M model,narrates the idea of arbitrage pricing and the risk-neutral pricing method.The parametric properties of SVI model and SABR model are also deduced.In application scenarios where time does not need to be considered for option prices,a simple and usable price approximation model is proposed.This model performs Taylor expansion of the classic model,uses ols regression to approximate the Taylor expansion of the classic model,and then passes the partial Piecewise,linear regression estimation parameters are linear optimization methods to calibrate the model.This method can bypass the nonlinear optimization problem of SVI model and SABR model parameter estimation.The empirical analysis is divided into two parts.The first part verifies the error between the price approximation model and the classic model.The price approximation model is a good approximation of the classic model regardless of whether it is the data of a certain day or the classical model.The second part verifies the pricing of more than 700 days of option data by the classic model and the approximate price model.Error analysis shows that in the option pricing problem within one day,the errors of the SVI model and the SABR model are much smaller than the B-S-M model.The error of the SVI model and the SABR model is close when β=1,and the error of the latter is slightly smaller than the former.At the same time,the error level of the price approximation model obtained by the price approximation method is close to that of the SABR model when β=1.The error of the former is smaller,and the error of the latter is even smaller.Both real-value call options have the same pricing error.The purpose of this article is to simplify the classic model.The SVI model,especially the SABR model,has a certain threshold for investors who have not received higher education.The complexity of the option pricing model also limits the ordinary people’s understanding of option contracts to a certain extent.The development and growth of the option market requires a broad mass base.After verification,the price approximation model in this paper is a simple pricing method with a pricing error within an acceptable range.