Julia Martínez-Rodríguez

Numerical investigation of the recruitment process in open marine population models

The changes in the dynamics, produced by the recruitment process in an open marine population model, are investigated from a numerical point of view. The numerical method considered, based on the representation of the solution along the characteristic lines, approximates properly the steady states of the model, and is used to analyze the asymptotic behavior of the solutions of the model.

Numerical analysis of an open marine population model with spaced-limited recruitment

A numerical method for an open marine population model with spaced-limited recruitment is presented. The method takes into account the singularity of the mortality rate at the finite maximum age, and it is based on the representation of the solution along the characteristics lines. We analyze the numerical scheme and use it to approximate the asymptotic behavior of the solutions of the model.

Estimation of risk-neutral processes in single-factor jump-diffusion interest rate models

The estimation of the market price of risk is an open question in the jump-diffusion term structure literature when a closed-form solution is not known. Furthermore, the estimation of the physical drift has a high risk of misspecification. In this paper, we obtain some results that relate the risk-neutral drift and the risk-neutral jump intensity of interest rates with the prices and yields of zero-coupon bonds. These results open a way to estimate the drift and jump intensity of the risk-neutral interest rates directly from data in the markets. These two functions are unobservable but their estimations provide an original procedure for solving the pricing problem. Moreover, this new approach avoids the estimation of the physical drift as well as the market prices of risk. An application to US Treasury Bill data is illustrated.

A new technique to estimate the risk-neutral processes in jump-diffusion commodity futures models

In order to price commodity derivatives, it is necessary to estimate the market prices of risk as well as the functions of the stochastic processes of the factors in the model. However, the estimation of the market prices of risk is an open question in the jump-diffusion derivative literature when a closed-form solution is not known. In this paper, we propose a novel approach for estimating the functions of the risk-neutral processes directly from market data. Moreover, this new approach avoids the estimation of the physical drift as well as the market prices of risk in order to price commodity futures. More precisely, we obtain some results that relate the risk-neutral drifts, volatilities and parameters of the jump amplitude distributions with market data. Finally, we examine the accuracy of the proposed method with NYMEX (New York Mercantile Exchange) data and we show the benefits of using jump processes for modelling the commodity price dynamics in commodity futures models.

Advances in pricing commodity futures: Multifactor models

Abstract The purpose of this paper is to obtain the risk-neutral drift of the state variables directly from market data in a multifactor commodity futures model. Note that the risk-neutral drift is a key factor in the general asset pricing theory but it is not observable. In this paper, we derive some exact results which relate the risk-neutral drifts to the slope of the commodity futures price jointly with the factors. This fact allows us to estimate some of the coefficients of the pricing partial differential equation directly from the futures data available in the markets. Moreover, we do not have to estimate either the physical drift or the market price of risk. Therefore we considerably reduce the number of functions to estimate and, as a consequence, we reduce the computational cost as well as the misspecification error. In order to investigate the finite sample properties of this approach we carry out some numerical experiments. Finally, an application to crude oil and natural gas futures contracts traded at the New York Mercantile Exchange (NYMEX) is also illustrated.

A multiplicative seasonal component in commodity derivative pricing

Abstract In this paper, we focus on a seasonal jump–diffusion model to price commodity derivatives. We propose a novel approach to estimate the functions of the risk-neutral processes directly from data in the market, even when a closed-form solution for the model is not known. Then, this new approach is applied to price some natural gas derivative contracts traded at New York Mercantile Exchange (NYMEX). Moreover, we use nonparametric estimation techniques in order to avoid arbitrary restrictions on the model. After applying this approach, we find that a jump–diffusion model allowing for seasonality outperforms a standard jump–diffusion model to price natural gas futures. Furthermore, we also show that there are considerable differences in the option prices and the risk premium when we consider seasonality or not. These results have important implications for practitioners in the market.

A new approach for pricing commodity futures contracts

In this article, we propose a new approach for pricing futures contracts more efficiently. We show that the coefficients of the pricing partial differential equation can be estimated directly from the data. We reduce the number of functions to be estimated as well as the computational cost. Finally, we carry out some numerical experiments.

The risk-neutral stochastic volatility in interest rate models with jump–diffusion processes

Abstract In this paper, we consider a two-factor interest rate model with stochastic volatility and we propose that the interest rate follows a jump–diffusion process. The estimation of the market price of risk is an open question in two-factor jump–diffusion term structure models when a closed-form solution is not known. We prove some results that relate the slope of the yield curves, interest rates and volatility with the functions of the processes under the risk-neutral measure. These relations allow us to estimate all the functions with the bond prices observed in the markets. Moreover, the market prices of risk, which are unobservable, can be easily obtained. Then, we can solve the pricing problem. An application to US Treasury Bill data is illustrated and a comparison with a one-factor model is shown. Finally, the effect of the change of measure on the jump intensity and jump distribution is analysed.

Real-World Versus Risk-Neutral Measures in the Estimation of an Interest Rate Model with Stochastic Volatility

In this paper, we consider a jump-diffusion two-factor model which stochastic volatility to obtain the yield curves efficiently. As this is a jump-diffusion model, the estimation of the market prices of risk is not possible unless a closed form solution is known for the model. Then, we obtain some results that allow us to estimate all the risk-neutral functions, which are necessary to obtain the yield curves, directly from data in the markets. As the market prices of risk are included in the risk-neutral functions, they can also be obtained. Finally, we use US Treasury Bill data, a nonparametric approach, numerical differentiation and Monte Carlo simulation approach to obtain the yield curves. Then, we show the advantages of considering the volatility as second stochastic factor and our approach in an interest rate model.

A numerical approach to obtain the yield curves with different risk-neutral drifts

In this paper we consider the possible dependence of the market price of risk on time and interest rates. This fact gives as a result that the risk-neutral drift, which is one of the coefficients of the pricing equation, also depends on time and interest rates. Then, we estimate the risk-neutral drift directly from the slope of the yield curve. This approach is very accurate as we show with a numerical experiment. In order to obtain the term structure we also propose a suitable finite difference method, which converges to the true solution. Finally, we obtain and compare the yield curves with data from the US Treasury Bill market.