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Dynamic Methods for Multivariate Option Pricing

Author: ZhangJing
Tutor: Dominique Guégan;ZhengWeiAn
School: East China Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: Option Valuation Risk Neutral Risk Premium GARCH Process GARCH-Normal Model GARCH-NIG Model Regime Switching Black-Scholes Model Call Option Dynamic Copula Goodness-of-Fit (GOF) Test Conditional Copula Binary Segmentation Change-point Time-varying Parameter function Call-on-max Option
CLC: F830.9
Type: PhD thesis
Year: 2008
Downloads: 480
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Abstract


Our work provides firstly a general discrete approach to construct the risk neutral transformation from the physical(objective)probability measure to the risk neutral probability measure in order to obtain the fair value of options.Thanks to this general risk neutralization model,a large class of conditionally non-Normal processes for underlying assets and a large class of time-varying risk-premium can be accommodated in a general transformation model.In addition,we show that the transformed conditional distribution function is of the same family as that of the original one as long as the moment generating function of the original distribution function exists,which is illustrated by two special cases:Normal distribution and Normal Inverse Gaussian(NIG)distribution.Our general risk neutralization model then is applied to price multivariate options.For the univariate case,we discuss two kinds of dynamic models:GARCH type model and regime switching model.Particularly,we use Normal and NIG conditional distribution functions respectively to combine these dynamic models. The empirical result concerning the European call option is compared with the result from the classical Black-Scholes model,which shows the advantages of our approach.As multivariate options are regarded as excellent tool for hedging the risk in today’s finance,we develop our dynamic method for multivariate option pricing. In order to study the dependence structure among the multi-assets,we apply the ideal dependence measure "copula".Considering that the dependence structure may change when the financial assets cover a long time period,we provide a dynamic copula method using conditional copulas,goodness-of-fit(GOF)test, binary segmentation procedure,change-point theory and time-varying functions. Through this dynamic method,the changes of the copula can be observed and we can detect two types of copula’s change:(1)the change of copula’s family and (2)the change of copula’s parameters with invariant copula’s family.In this way, the change-points either for the copula’s family or for the copula’s parameter are detected.When the dynamic copula is of static copula family,the dynamic evolution of the copula’s parameter can be determined by a time-varying function of predetermined variables,which gives a considerably dynamic expression to the changes of the copula and makes the changes of parameter more tractable.When using the dynamic copula method to price multivariate options,we derive a result that the physical copula and the risk neutral copula are the same under our general risk neutralization model.Therefore it is rather applicable to price multivariate options with our dynamic pricing method.We concern on pricing bivariate options,particularly,call-on-max options in the empirical work,and we compare different bivariate option pricing models,which presents our method’s advantages.

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CLC: > Economic > Fiscal, monetary > Finance, banking > Finance, banking theory > Financial market
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