We study the asymptotic behavior of the difference $\Delta \rho ^{X, Y}_\alpha := \rho _\alpha (X + Y) - \rho _\alpha (X)$ as $\alpha \rightarrow 1$, where $\rho_\alpha $ is a risk measure equipped with a confidence level parameter $0 < \alpha < 1$, and where $X$ and $Y$ are non-negative random variables whose tail probability functions are regularly varying. The case where $\rho _\alpha $ is the value-at-risk (VaR) at $\alpha $, is treated in Kato (2017). This paper investigates the case where $\rho _\alpha $ is a spectral risk measure that converges to the worst-case risk measure as $\alpha \rightarrow 1$. We give the asymptotic behavior of the difference between the marginal risk contribution and the Euler contribution of $Y$ to the portfolio $X + Y$. Similarly to Kato (2017), our results depend primarily on the relative magnitudes of the thicknesses of the tails of $X$ and $Y$. We also conducted a numerical experiment, finding that when the tail of $X$ is sufficiently thicker than that of $Y$, $\Delta \rho ^{X, Y}_\alpha $ does not increase monotonically with $\alpha$ and takes a maximum at a confidence level strictly less than $1$.
Asymptotic Analysis for Spectral Risk Measures Parameterized by Confidence Level. (arXiv:1711.07335v1 [q-fin.RM])
Quantum Duality in Mathematical Finance. (arXiv:1711.07279v1 [q-fin.MF])
Mathematical finance explores the consistency relationships between the prices of securities imposed by elementary economic principles. Commonplace among these are replicability and the absence of arbitrage, both essentially algebraic constraints on the valuation map from a security to its price.
read more...Influence of jump-at-default in IR and FX on Quanto CDS prices. (arXiv:1711.07133v1 [q-fin.CP])
We propose a new model for pricing Quanto CDS and risky bonds. The model operates with four stochastic factors, namely: hazard rate, foreign exchange rate, domestic interest rate, and foreign interest rate, and also allows for jumps-at-default in the FX and foreign interest rates. Corresponding systems of PDEs are derived similar to how this is done in Bielecki at al., 2005. A localized version of the RBF partition of unity method is used to solve these 4D PDEs. The results of our numerical experiments presented in the paper qualitatively explain the discrepancies observed in the marked values of CDS spreads traded in domestic and foreign economies.
Strict Local Martingales and Optimal Investment in a Black-Scholes Model with a Bubble. (arXiv:1711.06679v1 [q-fin.MF])
There are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework and the Johansen-Ledoit-Sornette (JLS) financial bubble model. Based on a class of models that embeds the JLS model and can exhibit strict local martingale behavior, we clarify the connection between these previously disconnected approaches. While the original JLS model is never a strict local martingale, there are relaxations which can be strict local martingales and which preserve the key assumption of a log-periodic power law for the hazard rate of the time of the crash. We then study the optimal investment problem for an investor with constant relative risk aversion in this model. We show that for positive instantaneous expected returns, investors with relative risk aversion above one always ride the bubble.
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Price Optimisation for New Business. (arXiv:1711.07753v1 [q-fin.CP])
This contribution is concerned with price optimisation of the new business for a non-life product. Due to high competition in the insurance market, non-life insurers are interested in increasing their conversion rates on new business based on some profit level. In this respect, we consider the competition in the market to model the probability of accepting an offer for a specific customer. We study two optimisation problems relevant for the insurer and present some algorithmic solutions for both continuous and discrete case. Finally, we provide some applications to a motor insurance dataset.
A New Approach for Solving the Market Clearing Problem With Uniform Purchase Price and Curtailable Block Orders. (arXiv:1711.07731v1 [q-fin.PR])
The European market clearing problem is characterized by a set of heterogeneous orders and rules that force the implementation of heuristic and iterative solving methods. In particular, curtailable block orders and the uniform purchase price (UPP) pose serious difficulties. A block is an order that spans over multiple hours, and can be either fully accepted or fully rejected. The UPP prescribes that all consumers pay a common price, i.e., the UPP, in all the zones, while producers receive zonal prices, which can differ from one zone to another. The market clearing problem in the presence of both the UPP and block orders is a major open issue in the European context. The UPP scheme leads to a non-linear optimization problem involving both primal and dual variables, whereas block orders introduce multi-temporal constraints and binary variables into the problem. As a consequence, the market clearing problem in the presence of both blocks and the UPP can be regarded as a non-linear integer programming problem involving both primal and dual variables with complementary and multi-temporal constraints. The aim of this paper is to present a heuristic-free, exact and computationally tractable model, which solves the market clearing problem in the presence of both curtailable block orders and the UPP. By resorting to an equivalent UPP formulation, the proposed approach results in a mixed-integer linear program, which is built starting from a non-linear integer bilevel programming problem. Numerical results using real market data are reported to show the effectiveness of the proposed approach.
Corporate payments networks and credit risk rating. (arXiv:1711.07677v1 [cs.SI])
Understanding the structure of interactions between corporate firms is critical to identify risk concentration and the possible pathways of propagation of financial distress. In this paper we consider the in- teraction due to payments and, by investigating a large proprietary dataset of Italian firms, we characterize the topological properties of the payment network. We then focus on the relation between the net- work of payments and the risk of firms. We show the existence of an homophily of risk, i.e. the tendency of firms with similar risk pro- file to be statistically more connected among themselves. This effect is observed both when considering pairs of firms and when consider- ing communities or hierarchies identified in the network. By applying machine learning techniques, we leverage this knowledge to show that network properties of a node can be used to predict the missing rating of a firm. Our results suggest that risk assessment should take quan- titatively into account also the network of interactions among firms.
Statistical properties of market collective responses. (arXiv:1711.07630v1 [q-fin.ST])
We empirically analyze the price and liquidity responses to trade signs, traded volumes and signed traded volumes. Utilizing the singular value decomposition, we explore the interconnections of price responses and of liquidity responses across the whole market. The statistical characteristics of their singular vectors are well described by the $t$ location-scale distribution. Furthermore, we discuss the relation between prices and liquidity with respect to their overlapping factors. The factors of price and liquidity changes are non-random when these factors are related to the traded volumes. This means that the traded volumes play a critical role in the price change induced by the liquidity change. In contrast, the two kinds of factors are weakly overlapping when they are related to the trade signs and signed traded volumes. Hence, an imbalance of liquidity is related to the price change.
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Valuation of equity warrants for uncertain financial market. (arXiv:1711.08356v1 [q-fin.PR])
In this paper, within the framework of uncertainty theory, the valuation of equity warrants is investigated. Different from the methods of probability theory, the equity warrants pricing problem is solved by using the method of uncertain calculus. Based on the assumption that the firm price follows an uncertain differential equation, the equity warrants pricing formula is obtained for uncertain stock model.
Asymmetric return rates and wealth distribution influenced by the introduction of technical analysis into a behavioral agent based model. (arXiv:1711.08282v1 [q-fin.GN])
Behavioral Finance has become a challenge to the scientific community. Based on the assumption that behavioral aspects of investors may explain some features of the Stock Market, we propose an agent based model to study quantitatively this relationship. In order to approximate the simulated market to the complexity of real markets, we consider that the investors are connected among them through a small world network; each one has its own psychological profile (Imitation, Anti-Imitation, Random); two different strategies for decision making: one of them is based on the trust neighborhood of the investor and the other one considers a technical analysis, the momentum of the market index technique. We analyze the market index fluctuations, the wealth distribution of the investors according to their psychological profiles and the rate of return distribution. Moreover, we analyze the influence of changing the psychological profile of the hub of the network and report interesting results which show how and when anti-imitation becomes the most profitable strategy for investment. Besides this, an intriguing asymmetry of the return rate distribution is explained considering the behavioral aspect of the investors. This asymmetry is quite robust being observed even when a completely different algorithm to calculate the decision making of the investors was applied to it, a remarkable result which, up to our knowledge, has never been reported before.
A New Interpretation of the Economic Complexity Index. (arXiv:1711.08245v1 [q-fin.EC])
The Economic Complexity Index (ECI) introduced by Hidalgo and Hausmann (2009) has been successful in explaining differences in GDP/capita and economic growth across countries. There has been confusion, however, about what it means and why it works. The ECI was originally motivated as an enhancement of diversity which is defined as the number of products a country is competitive in. However, the ECI is orthogonal to diversity. Nor is the ECI an eigenvalue centrality measure - in fact, the standard eigenvalue centrality measure applied to the export similarity matrix is equivalent to diversity. Instead we show that the ECI can be understood in terms of spectral clustering. It corresponds to an approximate solution to the problem of partitioning a graph into two parts in order to minimize the connections between the parts. It can also be viewed as an optimal one-dimensional ordering that clusters countries with similar exports together and minimizes the distance between countries. We present two empirical examples that involve regional employment in occupations and industries rather than exports, in which diversity fails to be a distinguishing feature of the data. These particular regional settings illustrate how the ECI can be useful even when diversity is not.
Polynomial Jump-Diffusion Models. (arXiv:1711.08043v1 [q-fin.MF])
We develop a comprehensive mathematical framework for polynomial jump-diffusions, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under exponentiation and subordination. We present a generic method for option pricing based on moment expansions. As an application, we introduce a large class of novel financial asset pricing models that are based on polynomial jump-diffusions.