In this notes, I argue and show that the so-called Efficient Markets Hypothesis (EMH) is no less than a false prophecy, the Black-Scholes-Merton (BSM) formula - a perfect rendition of EMH - no more than a parlor trick, and risk-neutral pricing models - generalisations of BSM - severe...

After Presenting the payoff, we will establish some methods to evaluate, hedge and risk manage the digital risk.This article is the first part of the answer. It is focus on the digital pricing and hedging

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The...

In this paper, we study the statistical properties of the moneyness scaling transformation by Leung and Sircar (2015). This transformation adjusts the moneyness coordinate of the implied volatility smile in an attempt to remove the discrepancy between the IV smiles for levered and unlevered ETF...

We propose a new method to estimate the empirical pricing kernel based on option data. We estimate the pricing kernel nonparametrically by using the ratio of the risk-neutral density estimator and the subjective density estimator. The risk-neutral density is approximated by a weighted kernel...

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The...

We propose a unified transform-based method, which we call the extended double spiral (EDS) method, for pricing arithmetic Asian options under general two-dimensional (2D) models that nest regime-switching Levy models, stochastic volatility (SV) models with Levy jumps, and time-changed Levy...

We provide an analytic model for valuing continuous barrier options. The model is manifestly arbitrage-free, exactly fits the implied volatility smile, and produces prices consistent with an underlying stochastic volatility dynamic

This paper introduces parallel computation for spread options using two-dimensional Fourier transform. Spread options are multi-asset options whose payoffs depend on the difference of two underlying financial securities. Pricing these securities, however, cannot be done using closed-form...

Finite difference schemes are the preferred tool for solving the partial differential equations that arise when pricing exotic derivatives. The schemes available up to now can achieve at most O(∆t²) accuracy in time and O(∆x²) accuracy in space when recovering instrument prices. We show how...