Pricing of spread options on stochastically correlated underlyings

Abstract

This report proposes a method to price spread options on stochastically correlated underlying assets. Therefore it provides a more realistic approach towards correlation structure. We generalize a constant correlation tree model developed by Hull (2002) and extend it by the notion of stochastic correlation. The resulting tree model is recombining and easy to implement. Moreover, the numerical convergence of our model is very fast. Our sensitivity analysis with respect to the stochastic correlation parameters shows that the constant correlation model systematically overprices spread options on two stochastically correlated underlying assets. Furthermore, we use our model to derive hedging parameters for the correlation of a spread option and show that the constant correlation model also overprices the hedging parameters.

A Note on the Impact of Parameter Uncertainty on Barrier Derivatives

“…These choices for the correlation can be traced back to transformations in the work of [18][19][20]. It should be pointed out that we could have also used the sampling distributions for variance and correlation (in a Gaussian setting).…”

Pricing of mountain range derivatives under a principal component stochastic volatility model

“…Proposition shows that this model captures, to the best of our knowledge, all stylized facts reported in the literature: starting with multifactor stochastic volatility (see in a univariate context), which comes from being a function of several factors V i ; leverage effect, which is a negative relationship between volatility and price changes and comes from negative values for ρ j in the equation for ; and stochastic instantaneous correlation between stocks ρ jk ( t ) . Indeed, it has been established that a changing correlation has a significant impact in the price of many derivatives . Nonzero instantaneous correlation between stocks’ volatilities, , is related to volatility co‐movements or volatility ‘spillovers’ .…”

Pricing two dimensional derivatives under stochastic correlation

“…Under a GBM model with constant correlation there exist no exact closed form expression for the price of a spread option except when K = 0, see [8]. This is the main reason for which the available literature on the subject is devoted to approximated methods like numerical integration, Monte Carlo, trees and approximated closed forms ([2], [4], [15]).…”

“…We obtain an expression for the price in terms of the average correlation during its lifetime which allows us to use some suitable approximations, expanding the technique in [3]. Some works introducing stochastic correlation in the pricing of financial derivatives are [9] and [4]. In [9] the author provides analytical properties of the correlation process as well as an approximation to the value of Quantos options under the assumption of constant volatility for the underlying.…”

“…This approximation not only lacks a set of bounds for the error but also limits the applicability of the idea to other derivatives. In [4], the price of an spread option was obtained under stochastic correlation using numerical methods based on multidimensional trees. In this paper we provide a framework for pricing two-dimensional derivatives under time dependent correlation together with a bound for the error and without the need for time-consuming numerical methods.…”