Arturo Leccadito

Option pricing under regime-switching jump-diffusion models

We present an explicit formula and a multinomial approach for pricing contingent claims under a regime-switching jump-diffusion model. The explicit formula, obtained as an expectation of Merton-type formulae for jump-diffusion processes, allows to compute the price of European options in the case of a two-regime economy with lognormal jumps, while the multinomial approach allows to accommodate an arbitrary number of regimes and a generic jump size distribution, and is suitable for pricing American-style options. The latter algorithm discretizes log-returns in each regime independently, starting from the highest volatility regime where a recombining multinomial lattice is established. In the remaining regimes, lattice nodes are the same but branching probabilities are adjusted. Derivative prices are computed by a backward induction scheme.

HERMITE BINOMIAL TREES: A NOVEL TECHNIQUE FOR DERIVATIVES PRICING

Edgeworth binomial trees were applied to price contingent claims when the underlying return distribution is skewed and leptokurtic, but with the limitation of working only for a limited set of skewness and kurtosis values. Recently, Johnson binomial trees were introduced to accommodate any skewness-kurtosis pair, but with the drawback of numerical convergence issues in some cases. Both techniques may suffer from non-exact matching of the moments of distribution of returns. A solution to this limitation is proposed here based on a new technique employing Hermite polynomials to match exactly the required moments. Several numerical examples illustrate the superior performance of the Hermite polynomials technique to price European and American options in the context of jump-diffusion and stochastic volatility frameworks and options with underlying asset given by the sum of two lognormally distributed random variables.

True Versus Spurious Long Memory: Some Theoretical Results and a Monte Carlo Comparison

A common feature of financial time series is their strong persistence. Yet, long memory may just be the spurious effect of either structural breaks or slow switching regimes. We explore the effects of spurious long memory on the elasticity of the stock market price with respect to volatility and show how cross-sectional aggregation may generate spurious persistence in the data. We undertake an extensive Monte Carlo study to compare the performance of five tests, constructed under the null of true long memory versus the alternative of spurious long memory due to level shifts or breaks.

Value at Risk and Expected Shortfall Improved Calculation Based on the Power Transformation Method

Value-at-risk (VaR), expected shortfall (ES), and similar risk measures are based on knowledge of the underlying probability distribution of portfolio value, and in particular its lower tail. The theory is well developed for the familiar normal/lognormal case, but it is well known that the normal does not match the actual returns observed on portfolios of stocks and other risky assets. Empirical distributions tend to have fatter tails and negative skewness. Two standard ways to deal with this problem are either to assume the returns are generated by a probability law with more flexibility about tail shape than the Gaussian, such as one of the Johnson family of distributions, or else to develop an empirical fit to the unknown density using a technique such as Gram–Charlier or Cornish–Fisher approximation. In both approaches, the density is chosen to match the moments of the empirical density from the data. In this article, the author follows the second approach but suggests that a better approximation can be obtained using a power transformation of a standard normal variable whose coefficients are selected to match the first four moments of observed returns. Applying the technique on S&P 500 Index returns, the power transformation consistently produces more accurate estimates of VaR and ES than the other methods.

Wave after Wave: Contagion Risk from Commodity Markets

The aim of this study is to investigate the possible contagion risk coming from energy, food and metals commodity markets and to assess risk spillovers from biofuel to food commodity markets and from crude oil to food markets. To this purpose, we use the delta Conditional Value-at-Risk ΔCoVaR) approach recently proposed by Adrian and Brunnermeier (2016) based on quantile regression. This novel methodology allows us first to identify a measure of contagion risk for energy, food and metals commodity markets, then to detect whether the risk contribution for a given market is significant, while distinguishing between tail events driven by financial factors, economic fundamentals or both, and finally, to assess whether the contagion effect of one market is significantly larger than the one of another market. The results show that energy, food and metals commodity markets transmit contagion within markets and there are spillovers from crude oil and biofuel to food markets. In particular, oil is systemically riskier than the other markets in causing economic instability. Oil is also more important than biofuel in affecting food markets. It emerges that contagion risk is mainly triggered by financial factors for energy and metal markets, while financial and economic fundamentals are relevant for food markets.

Compound option pricing under stochastic volatility

The paper proposes a flexible and computationally efficient lattice-based approximation for evaluating European and American compound options under stochastic volatility models. In comparison with the existing evaluation procedures, the method is more flexible because it may accommodate several stochastic volatility specifications of the asset price process, and more efficient because it is computationally faster in computing accurate compound option prices. The method is obtained as an extension of Costabile et al. (2012) discretisation, which consists in approximating the stochastic volatility process by a recombining binomial lattice, and considers the asset value as an auxiliary variable whose dynamics is captured by generating subsets of representative realisations to cover the range of possible asset prices at each time slice. The backward induction scheme based on a linear interpolation technique is adapted to compute both the underlying daughter option and the compound option prices. Numerical experiments confirm the method efficiency and accuracy.

A new method for generating approximation algorithms for financial mathematics applications

This paper describes a new technique that can be used in financial mathematics for a wide range of situations where the calculation of complicated integrals is required. The numerical schemes proposed here are deterministic in nature but their proof relies on known results from probability theory regarding the weak convergence of probability measures. We adapt those results to unbounded payoffs under certain mild assumptions that are satisfied in finance. Because our approximation schemes avoid repeated simulations and provide computational savings, they can potentially be used when calculating simultaneously the price of several derivatives contingent on the same underlying. We show how to apply the new methods to calculate the price of spread options and American call options on a stock paying a known dividend. The method proves useful for calculations related to the log-Weibull model proposed recently for empirical asset pricing.