We clarify the relations among different Fourier-based approaches to option pricing, and improve the B-spline probability density projection method using the sinh-acceleration technique. This allows us to efficiently separate the control of different sources of errors better than the FFT-based...

In this paper, we propose a general approximation framework for the valuation of (path-dependent) options under time-changed Markov processes. The underlying background process is assumed to be a general Markov process, and we consider the case when the stochastic time change is constructed from...

Swing options are a type of exotic financial derivative which generalize American options to allow for multiple early-exercise actions during the contract period. These contracts are widely traded in commodity and energy markets, but are often difficult to value using standard techniques due to...

This work reviews the literature on spline local basis methods for non-parametric density estimation. Particular attention is paid to B-spline density estimators which have experienced recent advances in both theory and methodology. These estimators occupy a very interesting space in statistics,...

This note provides closed-form expressions for spatial Greeks (Delta and Gamma) for discretely monitored realized variance swaps under several common parametric model assumptions. We derive closed-form results for stochastic volatility and exponential L´evy models, as well as some...

This chapter studies the problem of swing option pricing in a L\'evy driven market. Swing options, which are exotic derivatives commonly traded in energy markets, provide an interesting generalization of American options in which multiple early-exercise (swing) decisions are made during the life...

Hybrid equity-rate derivatives are commonly traded between financial institutions, but are challenging to price with traditional methods. Especially challenging are those contracts which involve an explicit interest rate (fixing) dependence in the cashflows, which stretches typical...

This work introduces two new financial derivatives into the finance literature. The first is the Return Barrier Option, which has emerged recently as a popular contract in the OTC markets. This contract is similar to a barrier option, but the knock-out event depends on an asset's returns, rather...

This work studies the valuation and optimal surrender of variable (equity-linked) annuities under a L\'evy-driven equity market with mortality risk. We consider a practical periodic fee structure which can vary over time, and is assessed as a proportion of the fund value. At maturity, the fund...