It is quite common in option pricing and risk management for Greeks to be computed through finite differences approximation (“bump-and-reprice”), due to simplicity, general applicability and acceptable accuracy (if bumping stepsize is properly selected). However this approach is time...

The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both...

Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic...

Local volatility models are widely used to manage many exotic options in a way consistent with available market prices of vanilla options. Once calibrated, a local volatility grid can be used in numerical methods such as PDE or Monte Carlo to price and hedge exotic options consistently with...

Low-latency real-time option analytics feeds provide tick-by-tick implied volatilities and greeks based on exchange data. In order for the Black-Scholes implied volatility surface to exhibit the empirically observed skew or smile, a stochastic volatility model can be used to compute the option...

This thesis develops a generic framework based on the Fourier transform for pricing and hedging of various options in equity, commodity, currency, and insurance markets. The pricing problem can be reduced to solving a partial integro-differential equation (PIDE). The Fourier Space Time-stepping...

We present the first step in a program to develop a comprehensive, unified equilibrium theory of asset and liability pricing. We give a mathematical framework for pricing insurance products in a multiperiod financial market. This framework reflects classical economic principles (like utility...

Tutorial on valuation of mortgage backed securities and collateralized mortgage obligations, including: - Structure of the mortgage market - Prepayment modeling - OAS analysis - Interest rate modeling - Numerical methods - Parallelization

This is a preprint of the chapter "Supercomputers" in the forthcoming book "High-Performance Computing in Finance: Problems, Methods, and Solutions", M.A.H. Dempster, J. Kanniainen, J. Keane, and E. Vynckier (Eds), Chapman and Hall/CRC, London, 2017. The chapter discusses the use of...

We analyze model risk for the pricing of barrier options. In contrast to existing literature, this paper is based on an empirical data set of over 40,000 bonus certificates to analyze the real market extent of model risk for traded barrier options instead of purely synthetic options. For this...