Pricing and hedging basket options with exact moment matching

Abstract

Theoretical models applied to option pricing should take into account the empirical characteristics of financial time series. In this paper, we show how to price basket options when the underlying asset prices follow a displaced log-normal process with jumps, capable of accommodating negative skewness and excess kurtosis. Our technique involves Hermite polynomial expansion that can match exactly the first m moments of the model-implied basket return. This method is shown to provide superior results for basket options not only with respect to pricing but also for hedging.

Mixed linear fractional boundary value problems

“…Similar kinds of questions also appear when looking at barrier options under one-dimensional Markov models, see [MP13]. It is natural to consider multi-dimensional versions of these, [LPT16], as investors often deal with basket options. A further natural appearance comes when considering portfolios of credit derivative obligations (CDO), which can be described by a Markov process in R k + .…”

Pricing European Basket Option Using the Standard Monte Carlo and Antithetic Variates

“…In this case, buying a basket option can be an optimal alternative because a basket option is an option whose payoff value depends on a group of (𝑛) assets [4]. Basket options are one of the most popular exotic options in the commodity and equity markets [5] and are typically traded over the counter [6]. The advantage of the basket option is its ability to efficiently hedge risk on multiple assets at the same time [7].…”