Black-Scholes
The Chebyshev method for the implied volatility
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.
Path independence of exotic options and convergence of binomial approximations
In this paper, the authors analyse the convergence of tree methods for pricing barrier and lookback options.
Deep hedging and the end of the Black-Scholes era
Quants are embracing the idea of ‘model free’ pricing and hedging
How AI could tear up risk modelling canon
BlackRock, MSCI, LFIS among firms looking to replace traditional, linear risk models
Podcast: Hans Buehler on deep hedging and harnessing data
Quant says a new machine learning technique could change the way banks hedge derivatives
JP Morgan turns to machine learning for options hedging
New models sidestep Black-Scholes and could slash hedging costs for some derivatives by up to 80%
Application of the Heath–Platen estimator in the Fong–Vasicek short rate model
In this paper, the authors construct a Heath-Platen-type Monte Carlo estimator that performs extraordinarily well compared with the crude Monte Carlo estimation.
Efficient conservative second-order central-upwind schemes for option-pricing problems
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.
Polynomial upper and lower bounds for financial derivative price functions under regime-switching
In this paper, the authors present a new approach to bounding financial derivative prices in regime-switching market models from both above and below.
Importance sampling applied to Greeks for jump–diffusion models with stochastic volatility
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.
Rogue traders versus value-at-risk and expected shortfall
VAR and ES are ineffective to deter rogue trading
Validation of profit and loss attribution models for equity derivatives
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.
What financialisation means for oil: Ilia Bouchouev of Koch
Investor demand now drives oil prices as much as physical fundamentals
Quant of the year: Jean-Philippe Bouchaud
Risk Awards 2017: Physicist takes on classic models with data and empirical research
Deconstructing correlation
Peter Austing introduces an analytic or semi-analytic valuation of basket options
Cross-dependent volatility
Julien Guyon introduces cross-dependent volatility models and calibrate them to market smiles
Small banks face rate options valuation model change
Negative rates causing pricing model rethink
CVA and FVA with liability-side pricing
Wujiang Lou calculates CVA and FVA abiding by the law of one price
FX volatility – An evolutionary story
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…
Cutting edge introduction: Funding holes in Black-Scholes
HSBC quant builds funding costs and haircuts into Black-Scholes option pricing formula