Option pricing when correlations are stochastic: an analytical framework

Abstract

Wishart processes, Best-of basket option, Stochastic correlation, FFT,

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

“…For example, implied correlation estimates can be extracted from traded spread options [46], best-of basket options [19], and quanto options [4]. Implied correlation estimates based on various multiasset products are discussed in Austing [2].…”

“…This model was generalized in Semeraro [44], Luciano and Semeraro [33], and Guillaume [21]. A stochastic correlation model was considered in Fonseca et al [19]. A framework for modeling dependence in finance using copulas was described in Cherubini et al [14].…”

“…Several papers consider the problem of measuring implied correlation between stock prices; see e.g. Fonseca et al [19], Tavin [46], Ballotta et al [4], and Austing [2]. Our approach is different in that we determine implied correlation estimates in the onefactor Lévy model using multi-asset derivatives consisting of many assets (30 assets for the Dow Jones).…”

A Note on the Impact of Parameter Uncertainty on Barrier Derivatives

“…As suggested by [29], we annualize the daily volatility by multiplying by the square root of 250 ≈ 5998 24 , which is the number of trading days instead of the number of calendar days. In the next step, we compute the needed parameters for the explicit model (6), as well as for the implicit model (2). Hence, we use a moving window approach to compute the parameters c, ρ and λ based on different non-overlapping samples of a window size k. Always starting from 31 December 2013 and going backwards in time, this approach results in a sample of size n = 5998 k .…”

“…The best solution to this challenge is a stochastic covariance model, as those stochastic matrices tackle both features, volatility and correlation, simultaneously (see [1][2][3]). In such a context, when it comes to the actual pricing of products, practitioners either determine model parameters from option prices (usually called calibration) or obtain the parameters from historical observations of the underlying (estimation methodology).…”