A numerical method to price options with moving barrier and time-dependent rebate is proposed. In particular, using the so-called Boundary Element Method, an integral representation of the barrier option price is derived in which one of the integrand function is not given explicitly but must be...

Recently, the advantages of conformal deformations of the contours of integration in pricing formulas were demonstrated in the context of wide classes of Levy models and the Heston model. In the present paper we construct efficient conformal deformations of the contours of integration in the...

The method here to price discretely monitored barrier options in both constant and time-varying volatility valuation frameworks uses a time-homogeneous Markov chain to approximate the underlying asset price process. It provides a natural framework for this pricing process because the discrete...

Investors often control risk exposure by trading options. This article studies the optimal strategy for liquidating an option position. Under both complete and incomplete market settings, we quantify the value of optimally timing to liquidate, and identify the situations where it is optimal to...

Due to the uncertainty in reality consists of randomness and fuzziness, we employ stochastic analysis and fuzzy set theory to explore the pricing of geometric Asian options. In the fuzzy stochastic world, the price of the underlying asset is assumed to follow a fuzzy stochastic process of which...

We examine the pricing of financial crash insurance during the 2007-2009 financial crisis in U.S. option markets, and we show that a large amount of aggregate tail risk is missing from the cost of financial sector crash insurance during the crisis. The difference in costs between...

We examine the pricing of financial crash insurance during the 2007-2009 financial crisis in U.S. option markets, and we show that a large amount of aggregate tail risk is missing from the cost of financial sector crash insurance during the crisis. The difference in costs between...

We propose a novel, fast, accurate parallel algorithm for pricing American options. We perform a thorough numerical analysis of existing methodologies and find that ours performs significantly better. The proposed method is stable, robust, and converges monotonically. We also show that the...

R&D is often a highly uncertain venture where experiments achieve successful outcomes on an extraordinarily rare basis. Just one successful product could change the future of a company; the discovery stage can often be an invaluable or disastrous experience. We develop a real R&D option model...

We study the estimation, the dynamics, and the predictability of option-implied risk-neutral moments (variance, skewness, and kurtosis) for individual stocks from various perspectives. We first show that it is in the estimation of the higher moments essential to use an interpolation with a...