In this paper, the authors propose a bivariate interpolation of the implied volatility surface based on Chebyshev polynomials. This yields a closed-form approximation of the implied volatility, which is easy to implement and to maintain.
In this paper, the authors analyse the convergence of tree methods for pricing barrier and lookback options.
Quants are embracing the idea of ‘model free’ pricing and hedging
BlackRock, MSCI, LFIS among firms looking to replace traditional, linear risk models
Quant says a new machine learning technique could change the way banks hedge derivatives
New models sidestep Black-Scholes and could slash hedging costs for some derivatives by up to 80%
In this paper, the authors construct a Heath-Platen-type Monte Carlo estimator that performs extraordinarily well compared with the crude Monte Carlo estimation.
In this paper, the authors propose improvements to the approach of Ramírez-Espinoza and Ehrhardt (2013) for option-pricing PDEs formulated in the conservative form.
Vibrato and automatic differentiation for high-order derivatives and sensitivities of financial options
This paper deals with the computation of second-order or higher Greeks of financial securities. It combines two methods, vibrato and automatic differentiation (AD), and compares these with other methods.
In this paper, the authors present a new approach to bounding financial derivative prices in regime-switching market models from both above and below.
In this paper, the authors develop a procedure to reduce the variance when numerically computing the Greeks obtained via Malliavin calculus for jump–diffusion models with stochastic volatility.
VAR and ES are ineffective to deter rogue trading
The aim of this paper is to validate profit and loss attribution generated by daily movements of option prices as seen through their Black–Scholes (Black and Scholes 1973) and Merton (1973) implied volatilities.
Pricing multidimensional financial derivatives with stochastic volatilities using the dimensional-adaptive combination technique
In this paper, the authors present a new and general approach to price derivatives based on the Black–Scholes partial differential equation (BS-PDE) in a multidimensional setting.
Investor demand now drives oil prices as much as physical fundamentals
Risk Awards 2017: Physicist takes on classic models with data and empirical research
Peter Austing introduces an analytic or semi-analytic valuation of basket options
Julien Guyon introduces cross-dependent volatility models and calibrate them to market smiles
Negative rates causing pricing model rethink
Wujiang Lou calculates CVA and FVA abiding by the law of one price
Sponsored feature: Commerzbank
The damped Crank–Nicolson time-marching scheme for the adaptive solution of the Black–Scholes equation
This paper deals with error estimators and mesh adaptation for a space-time finite element discretization of the basic Black-Scholes equation. An interesting modern numerical mathematical technique for a fundamental pricing equation in finance is…
HSBC quant builds funding costs and haircuts into Black-Scholes option pricing formula