Multi-asset Option Pricing Model Based On Pair Copula-GARCH-G Approach

Over the past decade or so, financial markets have witnessed constant innovations; besides standard European and American options, a great deal of Multi-asset options evolved from standard options has come out in the international derivative markets. Multi-asset options usually have two or three underlying assets. Multi-asset options have flexible contracts terms, are cheaper and less prone to manipulation, so they have become the most actively traded options in international financial markets. Multi-asset options are playing a huge role in arbitrage and speculation, risk management and stabilizing financial markets. Therefore, it’s of critical importance for all participants in option markets to properly price multi-assets options.Many of the traditional pricing methods were built on the assumed normal distributions. But in financial practice and studies, researchers have found that many data(log returns of assets) in financial markets do not display a bell-shaped curve known as normal distribution. When the log return of assets don’t have a normal distribution, applying a model based on normal distribution on it can lead to hazardous situation such as misconfiguration of portfolio, wrong estimation of Value at Risk(VaR) and huge deviation in the pricing of derivatives. In order to accurately price options, this dissertation applies broad distribution(such as GH and GBG) and GARCH model to capture the characteristics of fat tails, leptokurtosis, skewness and random fluctuations of the yields of financial assets; employ Copula method and Pair copula method to describe the nonlinear dependence structure of multiple underlying assets, integrate the price information of multiple underlying assets, create the joint probability density function of multiple financial assets, and construct a Pair copula-GARCH-G model for pricing multi-assets options by applying martingale principle of risk-neutral pricing. This dissertation consists of three main sections below.Part one of the dissertation analyzes the dynamic evolution of asset prices. To achieve a more accurate description of assets’ characteristics of fat tails, leptokurtosis, skewness and random fluctuations, this part creates a GARCH-G process based on broad distribution to capture the dynamic evolution of asset prices. This approach expands the scope of the traditional GARCH-GAUSS process. Empirical Analysis with transaction data has shown that GARCH-G process is better than GARCH-GAUSS process at capturing the characteristics of fat tails, leptokurtosis, and skewness of assets. When the GARCH-G process is used to price options, it produces smaller errors than GARCH-GAUSS process.In Part two we integrate the price information of multiple underlying assets(create joint distribution function). To price Multi-asset options with martingale pricing techniques, we have to describe the joint distribution of multiple underlying assets and integrate the price information of these assets. In this part, we apply Pair copula techniques to describe the complex nonlinear dependence structure of assets, build a flexible joint distribution function of multiple underlying assets and integrate the price information of underlying assets. To test the effectiveness of Copula and Pair copula techniques in integrating price information of underlying assets, we use financial market data to conduct an empirical analysis of the calculation of optimal hedge ratio and VaR.Part three demonstrates the construction of Pair copula-GARCH-G model for pricing multi-asset options. Also, the third part is the empirical analysis of Pair copula-GARCH-G multi-asset option pricing model. After having analyzed the dynamic evolution of asset prices and integrated the price information of multiple underlying assets, we employ the martingale principle of risk-neutral pricing to build an options pricing model based on broad- distribution multiple assets. We describe the dynamic evolution of underlying assets with GARCH-G model; capture the characteristics of fat tails, leptokurtosis, skewness and random fluctuations of assets, build a joint distribution function of multiple underlying assets, integrate the price information of underlying assets, and finally, construct a Copula-GARCH model for pricing multi-assets options by applying martingale principle of risk-neutral pricing. Meanwhile, the detailed procedures are given of using Monte Carlo simulation techniques to evaluate multiple assets. Multiple foreign exchange options involve a variety of complex relationships between monetary exchange rate, and they can be seen as fused together by standard options in multiple currencies. Multiple foreign exchange options can effectively control the risk of multiple exchange rates between currencies. In this part, we used Pair copula-GARCH-G multi-asset option pricing model to evaluate the Mutiple Forex Option(RMB index options). The results showed that the Pair copula-GARCH multi-asset option pricing model had advantages.