It is well known that the correlation between financial products or financial institutions, e.g. plays an essential role in pricing and evaluation of financial derivatives. Using simply a constant or deterministic cor...
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It is well known that the correlation between financial products or 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 correlation is not a deterministic quantity. In this work, we propose a new approach to model the correlation as a hyperbolic function of a stochasticprocess. Our general approach provides a stochasticcorrelation which is much more realistic to model real- world phenomena and could be used in many financial application fields. Furthermore, it is very flexible: any mean-reverting process (with positive and negative values) can be regarded and no additional parameter restrictions appear which simplifies the calibration procedure. As an example, we compute the price of a Quanto applying our new approach. Using our numerical results we discuss concisely the effect of considering stochasticcorrelation on pricing the Quanto.
correlation plays an important role in pricing multi-asset options. In this work we incorporate stochasticcorrelation into pricing quanto options which is one special and important type of multi-asset option. Motivat...
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correlation plays an important role in pricing multi-asset options. In this work we incorporate stochasticcorrelation into pricing quanto options which is one special and important type of multi-asset option. Motivated by the market observations that the correlations between financial quantities behave like a stochasticprocess, instead of using a constant correlation, we allow the asset price process and the exchange rate process to be stochastically correlated with a parameter which is driven either by an Ornstein-Uhlenbeck process or a bounded Jacobi process. We derive an exact quanto option pricing formula in the stochasticcorrelation model of the Ornstein-Uhlenbeck process and a highly accurate approximated pricing formula in the stochasticcorrelation model of the bounded Jacobi process, where correlation risk has been hedged. The comparison between prices using our pricing formula and the Monte-Carlo method are provided.
The degree of relationship between financial products and financial institutions, e.g. must be considered for pricing and hedging. Usually, for financial products modeled with the specification of a system of stochast...
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The degree of relationship between financial products and financial institutions, e.g. must be considered for pricing and hedging. Usually, for financial products modeled with the specification of a system of stochastic differential equations, the relationship is represented by correlated Brownian motions (BMs). For example, the BM of the asset price and the BM of the stochastic volatility in the Heston model correlates with a deterministic constant. However, market observations clearly indicate that financial quantities are correlated in a strongly nonlinear way, correlation behaves even stochastically and unpredictably. In this work, we extend the Heston model by imposing a stochasticcorrelation given by the Ornstein-Uhlenbeck and the Jacobi processes. By approximating nonaffine terms, we find the characteristic function in a closed-form which can be used for pricing purposes. Our numerical results and experiment on calibration to market data validate that incorporating stochasticcorrelations improves the performance of the Heston model.
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