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In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swap option price in a probability setting equipped with a subfiltration structure. The Euler-Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical algorithm for pricing. Finally, the Antithetic Variable technique is used to reduce the variance of credit default swap option prices.

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Among the characterizing features of a time series, a relevant role is played by the so-called persistence or long-term memory property. Such aspect is related to the autocorrelation of the time series, and reflects the behavior of the process on the long-run. Hurst (1951) has been the pioneer of the formalization of the concept of long-term memory property for a hydrological time series. The persistence property of a time series has a relevant informative content in many applied contexts. This paper deals with one of the most prominent one. In fact, we consider the series of deviation of the price of a portfolio of commodities from a reference commodity. In so doing, we explore the long-term memory properties of a so-called mispricing portfolio of commodities. The selected commodities are crude oils. Yet, the persistence properties of a mispricing portfolio of crude oils explains the replicability of the reference oil price dynamics through the non-reference oils. This is of paramount importance in many respects, like hedging and assessing statistical arbitrage effects. In general, the exploration of the long-run behavior of a time series brings key information on if and how the related phenomenon can be predicted (see e.g.:

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