Abstract
This work deals with the stochastic modelling of correlation in finance. It is well known that the correlation between financial products, financial institutions, e.g., plays an essential role in pricing and evaluation of financial derivatives. Using simply a constant or deterministic correlation may lead to correlation risk, since market observations give evidence that the correlation is hardly a deterministic quantity. For example, we illustrate this issue with the analysis of correlation between daily returns time series of S&P Index and Euro/USD exchange rates. The approach of modelling the correlation as a hyperbolic function of a stochastic process has been recently proposed. Here, we review this novel concept and generalize this approach to derive stochastic correlation processes (SCP) from a hyperbolic transformation of the modified Ornstein-Uhlenbeck process. We determine a transition density function of this SCP in closed form which could be used easily to calibrate SCP models to historical data. As an illustrating example of our new approach, we compute the price of a quantity adjusting option (Quanto) and discuss concisely the effect of considering stochastic correlation on pricing the Quanto.
Highlights
Correlation is a well established concept for quantifying the relationship between financial assets
A more general stochastic correlation process was proposed by Teng et al [ ], which relies on the hyperbolic transformation with the hyperbolic tangent function of any mean-reverting process with positive and negative values, the properties (i)-(iii) above can be directly satisfied without facing any additional parameter restrictions
Instead of assuming a constant correlation, correlation has to be modelled as a stochastic process
Summary
Correlation is a well established concept for quantifying the relationship between financial assets. A more general stochastic correlation process was proposed by Teng et al [ ], which relies on the hyperbolic transformation with the hyperbolic tangent function of any mean-reverting process with positive and negative values, the properties (i)-(iii) above can be directly satisfied without facing any additional parameter restrictions. 2.1 The transformed mean-reverting process For the motivations and the properties (i)-(iii) in Section , Teng et al [ ] proposed the hyperbolic tangent function of a mean-reverting stochastic process Xt, like the OrnsteinUhlenbeck process [ ] or the square root diffusion processes (with positive and negative values) dXt = a(t, Xt) dt + b(t, Xt) dWt, t ≥ , X = x , to model the correlations as ρt = tanh(Xt), ρ = tanh(x ) ∈ (– , ).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
