We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to...

This paper presents a tailor-made discrete-time simulation model for valuing path-dependent options, such as lookback option, barrier option and Asian option. In the context of a real-life application that is interest to many students, we illustrate the option pricing by using Quasi Monte Carlo...

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...

We consider the problem of reducing the variance of Monte Carlo estimators of multivariate estimation problems by combining the variance reduction techniques Latin hypercube sampling with dependence (LHSD), control variates and importance sampling. Under some standard conditions, the resulting...

A credit-linked note (CLN) on a tranche of the CDX index (partially) protects the holder against default losses in that tranche. The holder receives a specified redemption amount at note maturity. The note is priced using market spread quotes for a matching CDS on this tranche

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...

We present an embarrassingly simple method for supervised learning of SABR model's European option price function based on lookup table or rote machine learning. Performance in time domain is comparable to generally used analytic approximations utilized in financial industry. However, unlike the...

In this paper we develop efficient Monte Carlo methods for estimating American option sensitivities. The problem can be re-formulated as how to perform sensitivity analysis for a stochastic optimization problem when it has model uncertainty. We introduce a generalized infinitesimal perturbation...

In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate...