A meshfree approximation scheme based on the radial basis function methods is presented for the numerical solution of the options pricing model. This thesis deals with the valuation of the European, Barrier, Asian, American options of a single asset and American options of multi assets. The option prices are modeled by the Black-Scholes equation. The θ-method is used to discretize the equation ...

This paper proposes an analytical approximation to price exotic options within a stochastic volatility framework. Assuming a general mean reverting process for the underlying asset and a square-root process for the volatility, we derive an approximation for option prices using a Taylor expansion around two average defined volatilities. The moments of the average volatilities are computed analyt...

High-frequency trading and automated algorithm impose high requirements on computational methods. We provide a model-free option pricing approach with neural networks, which can be applied to real-time pricing and hedging of FX options. In contrast to well-known theoretical models, an essential advantage of our approach is the simultaneous pricing across different strike prices and parsimonious...

Option pricing plays an important role in financial,energy, and commodity markets. The Black-Scholes model is an indispensable framework for the option pricing. This thesis studies the pricing of a swing option under stochastic volatility. A swing option is an American-style contract with multiple exercise rights. As such, it is an optimal multiplestopping time problem. In this dissertation, we...

Derivative securities, when used correctly, can help investors increase their expected returns and minimize their exposure to risk. Options offer leverage and insurance for risk-averse investors. For the more risky investors, they can be ways of speculation. When an option is issued, we face the problem of determining the price of a product which depends on the performance of another security a...

We give explicit upper bounds for convergence rates when approximating both oneand two-sided general curvilinear boundary crossing probabilities for the Wiener process by similar probabilities for close boundaries of simpler form, for which computation of the boundary crossing probabilities is feasible. In particular, we partially generalize and improve results obtained by Pötzelberger and Wang...

This paper proposes the sample path generation method for stochastic volatility version of CGMY process. We present Monte-Carlo European and American option pricing with calibrate model parameters to style S&P 100 index options market, using least square regression method. Moreover, we discuss path-dependent options, such as Asian Barrier options.

In this paper we propose a general foreign equity option pricing framework that unifies the vast foreign equity option pricing literature and incorporates the stochastic volatility into foreign equity option pricing. Under our framework, the time-changed Lévy processes are used to model the underlying assets price of foreign equity option and the closed form pricing formula is obtained through ...

As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others i...