{"title":"一般Garch-in-Mean模型的期权估值公式","authors":"Z. Qian, Xingcheng Xu","doi":"10.2139/ssrn.3185994","DOIUrl":null,"url":null,"abstract":"We derive option pricing formulas based on general GARCH-M models by using risk-neutral arguments. These formulas are beautiful in nature and realistic for applications. We propose a parameter estimation procedure and employ Monte Carlo method to evaluate the price. Demonstrations of these formulas applying to S&P 500 index options are shown. Empirical evidence suggests that both in U.S. stock market and Chinese financial market the performances of these theoretical pricing formulas are better than the results via Black-Scholes' pricing formula with constant volatility.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Option Valuation Formula for General Garch-in-Mean Models\",\"authors\":\"Z. Qian, Xingcheng Xu\",\"doi\":\"10.2139/ssrn.3185994\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We derive option pricing formulas based on general GARCH-M models by using risk-neutral arguments. These formulas are beautiful in nature and realistic for applications. We propose a parameter estimation procedure and employ Monte Carlo method to evaluate the price. Demonstrations of these formulas applying to S&P 500 index options are shown. Empirical evidence suggests that both in U.S. stock market and Chinese financial market the performances of these theoretical pricing formulas are better than the results via Black-Scholes' pricing formula with constant volatility.\",\"PeriodicalId\":260073,\"journal\":{\"name\":\"Mathematics eJournal\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics eJournal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2139/ssrn.3185994\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics eJournal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3185994","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Option Valuation Formula for General Garch-in-Mean Models
We derive option pricing formulas based on general GARCH-M models by using risk-neutral arguments. These formulas are beautiful in nature and realistic for applications. We propose a parameter estimation procedure and employ Monte Carlo method to evaluate the price. Demonstrations of these formulas applying to S&P 500 index options are shown. Empirical evidence suggests that both in U.S. stock market and Chinese financial market the performances of these theoretical pricing formulas are better than the results via Black-Scholes' pricing formula with constant volatility.
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