General closed-form basket option pricing bounds

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms, hence they do not suffer from the curse of dimensionality and can be applied also to high dimensional problems where most existing methods fail. In particular we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate. Permanent repository link

Testing for normality in any dimension based on a partial differential equation involving the moment generating function

“…As a result, testing the hypothesis that observed financial log-returns follow a multivariate normal law is of interest when pricing basket options. For more details regarding the pricing of these options, the interested reader is referred to [8].…”

Affine Multiple Yield Curve Models

“…call) option on a coupon bond. In this subsection, by relying on Fourier methods and along the lines of [9,10], we provide a general analytical approximation which exploits the affine property of our framework. We work in the general setting of Section 3.2, noting that all formulas admit suitable simplifications in the case of affine short-rate multi-curve models.…”

Accurate Pricing of Swaptions via Lower Bound

“…Another important fact is that our lower bound formula is very suitable to be used as a control variate to reduce Monte Carlo error. The approximated formula is easy to implement in a Monte Carlo scheme and turns out to be very effective (see Caldana, Fusai, Gnoatto and Grasselli (2014) for details). Swaption prices for different tenor and maturities are reported in Tables (1-5) with the relative overall computing time for each pricing method.…”