Exotic Option Pricing Based On Constrained Canonical Valuation

Option is a popular financial derivative,and the study of the option price is always an important issue of financial asset pricing theory.With the continuous development of China’s financial market,the option trading has gradually promoted,thus the research of an option pricing method adapt incomplete market has important practical significance.Stutzer(1996)put forward the Canonical Valuation,which is a non-parametric option pricing method,avoiding the parameters hypothetical questions in traditional option pricing methods.And unlike most non-parametric methods pricing new option from the other option prices,the Canonical Valuation just start from the historical trading prices of the underlying asset to get the yield data,and use relative entropy to calculate the risk-neutral probability,and then price the new option.Therefore,even in the incomplete market that options trading price is unreliable,unavailable,or even non-existent,this method also can efficiently price options.Existing research about the Canonical Valuation mainly in European and American option pricing,this article extends the method to path-dependent exotic option pricing.At present,there are three types of path-dependent exotic options:Asian options,lookback options and barrier options.This article research the pricing of geometric average price call option,fixed lookback put option and down-and-out call option to illustrate the pricing effect of Canonical Valuation on path-dependent exotic options.And taking the European call option and American put option as constraints through a comparative analysis,thus construct the Constrained Canonical Valuation.In the numerical experiment,I simulate the stock price paths to get the yield matrix of the underlying asset,and calculate European call option price with Black-Scholes formula,American put option price with binary method,and then get the exotic option prices by Matalab programming.The Monte Carlo simulation method was used to calculate the theoretical value,and calculate the errors between the estimated value and the theoretical value.Through data analysis,the pricing error was reduced after adding constraints to the Canonical Valuation,and the effect is best while adding both the European call and American put options.Thus illustrate that the Canonical Valuation is feasible for exotic option pricing,and adding constraints can improve the pricing accuracy.This study provides a viable option for pricing path-dependent exotic options,the main advantages of the method can be concluded as that,it needn’t to make any assumptions,can efficiently price options even in the incomplete market,and it is easy to understand in theory,easy to obtain the calculation result by programming.