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 general purpose technique for the efficient and accurate valuation of options in the shifted Stochastic Alpha Beta Rho (shifted-SABR) model which includes SABR as a special case. The method is based on a novel double-layer continuous-time Markov chain (CTMC) from which closed-form...

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...

After the financial crisis, a financial innovation, the central clearing counterparty (CCP) has been proposed and proved its importance in facilitating the clearing of interbank liabilities. In its original design, there is a possibility that the CCP may go default, and thus jeopardizing the...

In this paper, we propose a theoretical and computational framework for the detection and identification of (triangular) arbitrage opportunities among spot currency exchange rates in a foreign exchange market. We obtain sufficient conditions for excluding the triangular arbitrage opportunities...

We consider estimating an expected infinite-horizon cumulative cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random horizon is proposed. Explicit forms for the optimal distributions of the...

We obtain exact semi-explicit solutions to the optimal pricing problem for the multinomial logit (MNL) consumer choice model with network effects, through a novel conditioning argument and the use of the Lambert W function. Then we manage to characterize the exact optimal solution in the...

We propose a novel graph-theoretic method for the detection of circular arbitrage in foreign exchange (FX) markets and discuss and demonstrate runtime improvements of this algorithm over the brute force approach. An application on empirical currency bid/ask price data validates this technique as...

We establish a novel duality relationship between continuous and discrete non-negative additive functionals of stochastic (not necessarily Markovian) processes and their right inverses. For general Markov processes, we further extend and develop a theoretical and computational framework for the...

This paper establishes the second-order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing continuously monitored occupation time derivatives (step options, conditional Asian options) and arithmetic Asian options and their Greeks. We fill the gap in the...