The multivariate lognormal model is a basic pricing model for derivatives with multiple underlying processes, for example, spread options. However, the market observation of implied correlation skew examplifies how inaccurate the constant correlation assumption in the multivariate lognormal model can be. In this dissertation, we study alternative modeling approaches that generate implied correlation skews while at the same time maintain practical tractability.;First, we propose a multiscale stochastic volatility model, and derive asymptotic formulas for option valuation and implied correlation. The model is a two-dimensional extension of the multiscale stochastic volatility model proposed in [1] which was tested on single underlying options. To obtain option valuations, we only need to calibrate a set of special parameters, and we propose a calibration procedure using option prices on individual underlying assets. From our simulated results, the multiscale stochastic volatility model generates implied correlation skews, and the asymptotic formulas are easy and fast to implement.;In the multiscale stochastic volatility model, the stochastic volatilities introduce non-tradable sources of risk, and the market is no longer complete. Alternatively, we propose a local correlation model, which assumes the instantaneous correlation to be a deterministic function of time and the underlying prices. This model can be viewed as a two-dimensional extension of Dupire's local volatility model. The local correlation approach preserves the completeness of the market and low dimensionality of uncertainty.
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