Levy Option Monte Carlo Pricing

After the2008financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly.In this context, a review of the China's warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China's financial market environment.Black-Scholes model and other traditional option pricing models are usually built on the assumption of normal distribution of financial assets under yields, and the strong non-normal characteristics of financial data have been confirmed, thus Levy stochastic processes can correct the traditional model by improving pricing accuracy. Levy processes are collectively referred to the distribution function with independent increments, steady incremental and stochastically continuous characteristics, it is widely used in finance, medicine, physics and other fields. Levy can be expressed in higher-order statistical features especially assets "jump feature" and "asymmetric characteristics". However, compared with the normal random model, Structures of Levy stochastic models are more complex, Levy model parameter estimation, and risk-neutral measure conversion and random number generation are more difficult, is not suitable to solve the path-dependent option pricing problems. But random number generating algorithm is a core issue for Monte Carlo simulation.In this paper, Levy stochastic process with several traditional option pricing models for correction and expansion are discussed, while a comprehensive empirical research on China's mainland European Style Warrants, American and Bermudan Warrants. The specific content and related results are as follows:1In the framework of Monte Carlo simulation pricing, we established multi-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models.2Option pricing is sensitivity to assets volatility, taking into account the time-varying characteristics of the financial assets, we use biased GARCH model to model the underlying assets while introducing Levy stochastic process to model the "innovations". China warrants trading data are used to do empirical verify for these models It is proved the Levy-GARCH models can describe the historical volatility of the time-varying data characteristics.3For the path-dependent American option pricing problem, we use Levy-GARCH models to simulate price path of underlying assets, based on American option lest square Monte Carlo method we calculate expected cash flows iteratively, then with the Monte Carlo simulation method we obtained the option pricing result. The empirical research of American Style China's Warrants and Bermuda data confirmed the effectiveness of this approach.4We introduced a variance reduction technology modified with change Brownian motion Levy random number generation algorithm. First we generate two highly correlated random path, one normal distribution path and one Levy path, then we used random path to simulate the control variable. Under the framework of control variable algorithm, we introduced this "variance reduction method under Levy processes". Finally, we use this method to simulate European China's warrants, the results verified analog path can reduce the variance between samples, this method can accelerate the convergence speed of Monte-Carlo simulation.