The purpose of this project is to extend the Heston model in order to incorporate the term structure (TS) of the implied volatility surface. This includes implementing a TS within the Heston model and its calibration to a set of market instruments. The TS Heston model with piecewise constant parameters is implemented to match the TS and the COS pricing method is used for fast option pricing. We...

We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier cosine series expansion, as in [9, 10], and high-order quadrature rules in the other dimension. Error analysis and experiments confirm a fast error conver...

We propose an iterative method for pricing American options under jumpdiffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration...

In the following paper, we provide a review and development of sequential Monte Carlo (SMC) methods ([17, 18, 24]) for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used, successfully, for a wide class of applications in engineering, statistics and physic...

We propose a stable nonparametric method for constructing an option pricing model of exponential Lévy type, consistent with a given data set of option prices. After demonstrating the ill-posedness of the usual and least squares version of this inverse problem, we suggest to regularize the calibration problem by reformulating it as the problem of finding an exponential Lévy model that minimizes ...

We propose a stable nonparametric method for constructing an option pricing model of exponential Lévy type, consistent with a given data set of option prices. After demonstrating the ill-posedness of the usual and least squares version of this inverse problem, we suggest to regularize the calibration problem by reformulating it as the problem of finding an exponential Lévy model that minimizes ...

We propose a stable nonparametric method for constructing an option pricing model of exponential Lévy type, consistent with a given data set of option prices. After demonstrating the ill-posedness of the usual and least squares version of this inverse problem, we suggest to regularize the calibration problem by reformulating it as the problem of finding an exponential Lévy model that minimizes ...

Barrier options are cheaper than the respective standard European options, because a zero payoff may occur before expiry time T. Lower premiums are usually offered for more exotic barrier options, which make them particularly attractive to hedgers in the financial market. Under the Black-Scholes framework, we explicitly derive and present pricing formulae for a range of different European barri...

In this thesis I discuss the method of time-change and its applications in quantitative finance. I mainly consider the time change by writing a continuous diffusion process as a Brownian motion subordinated by a subordinator process. I divide the time change method into two cases: deterministic time change and stochastic time change. The difference lies in whether the subordinator process is a ...