This paper investigates the pricing of single-asset autocallable barrier reverse convertibles in the Heston local-stochastic volatility (LSV) model. Despite their complexity, autocallable structured notes are the most traded equity-linked exotic derivatives. The autocallable payoff embeds an...

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...

Unlike tranches of synthetic CDOs, that depend only on the defaults of the underlying securities, tranches of cashflow CDOs also depend on the interest cash flows from the coupons of the securities. Whilst fast, accurate, (semi-)analytic methods exist for pricing synthetic CDO tranches (Hull and...

We combine the multilevel Monte Carlo (MLMC) method with the numerical scheme for the Heston model that simulates the variance process exactly or almost exactly and applies the stochastic trapezoidal rule to approximate the time-integrated variance process within the SDE of the logarithmic asset...

Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which cannot be computed by direct Monte Carlo methods. Least...

Investment behaviour, techniques and choices have evolved in the options markets since the launch of options trading in 1973. Today, we are entering the field of Big Data and the explosion of information, which has become the main feature of science, impacts investors' decisions and their...

The main goal of this paper is to better understand the behavior of credit spreads in the past and the potential risk of unexpected future credit spread changes. One important consideration to note regarding credit spreads is the fact that bond spreads contain a liquidity premium, which...

We model the joint dynamics of stock and interest rate by a hybrid SABR-Hull-White model, in which the asset price dynamics are modeled by the SABR model and the interest rate dynamics by the Hull-White short-rate model. We propose a projection formula, mapping the SABR-HW model parameters onto...

This paper discusses how to obtain the Black-Scholes equation to evaluate options and how to obtain explicit solutions for Call and Put. The Black-Scholes equation, which is the basis for determining explicit solutions for Call and Put, is a rather sophisticated equation. It is a partial...