This paper extends and refines the method of option pricing by frame projection of risk-neutral densities to incorporate general B-splines, including the cubic basis, and general payoff structures. We introduce a coefficient stabilization method which substantially improves convergence for...

This paper introduces a novel method to price arithmetic Asian options in Levy-driven models, with discrete and continuous averaging, by expanding on the approach of sequential characteristic function recovery. By utilizing frame duality and a FFT-based implementation of density projection, we...

We develop a method for efficiently inverting analytic characteristic functions using frame projection, as in the case of Heston's model and exponential Levy models. Utilizing the duality theory of Riesz bases, we derive analytical formulas for coefficients of the orthogonally projected density,...

We present an efficient method for robustly pricing discretely monitored barrier and occupation time derivatives under exponential Levy models. This includes ordinary barrier options, as well as (resetting) Parisian options, delayed barrier options (also known as cumulative Parisian or Parasian...

In this paper, we propose a new non-parametric density estimator derived from the theory of frames and Riesz bases. In particular, we propose the so-called bi-orthogonal density estimator based on the class of B-splines, and derive its theoretical properties including the asymptotically optimal...

We present a new method to sample random variables through the use of orthogonal polynomial expansions of the associated quantile function that utilize the inverse transform technique. In particular, we obtain an explicit representation of the quantile function through an orthogonal expansion...

In this paper, we propose a general framework for the valuation of options in stochas-tic local volatility (SLV) models with a general correlation structure, which includes the Stochastic Alpha Beta Rho (SABR) model and the quadratic SLV model as special cases. Standard stochastic volatility...

In this paper, we develop a novel and efficient transform-based method to price equity-linked annuities (ELAs), including equity-indexed annuities (EIAs) and cliquet-style payoff structures popular in the insurance market under a general class of stochastic volatility models with jumps. We...

In this paper, we derive a closed-form explicit model-free formula for the (Black-Scholes) implied volatility. The method is based on the novel use of the Dirac Delta function, corresponding delta families, and the change of variable technique. The formula is expressed through either a limit or...

In this paper, we propose a general data-driven framework that unifies the valuation and risk measurement of financial derivatives, which is especially useful in markets with thinly-traded derivatives. We first extract the empirical characteristic function from market-observable time series for...