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Abstract: Abstract Inspired by the classical riot model proposed by Granovetter in 1978, we consider a parametric stochastic dynamical system that describes the collective behavior of a large population of interacting agents. By controlling a parameter, a policy maker seeks to minimize her own disutility, which in turn depends on the steady state of the system. We show that this economically sensible optimization is ill-posed and illustrate a novel way to tackle this practical and formal issue. Our approach is based on the \(\Gamma \) -convergence of a sequence of mean-regularized instances of the original problem. The corresponding minimum points converge toward a unique value that intuitively is the solution of the original ill-posed problem. Notably, to the best of our knowledge, this is one of the first applications of \(\Gamma \) -convergence in economics. PubDate: 2022-07-02
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Abstract: Abstract In this note, we point out a mistake in Theorem 1 of De De Gennaro Aquino and Bernard (Decis Econ Finance 42(2):715–741, 2019) and provide some missing references where the problem of pricing barrier options under the Heston model had previously been discussed. PubDate: 2022-06-01
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Abstract: Abstract The standard problem of portfolio choice between one risky and one riskless asset is analyzed in the model of expected utility with a safety-first component that is represented by the probability of final wealth exceeding a “safety” wealth level. It finds that a positive expected excess return remains sufficient for investing a positive amount in the risky asset except in the special situation where the safety wealth level coincides with the wealth obtained when the entire initial wealth is invested in the riskless asset. In this situation, the optimal amount invested in the risky asset is zero if the weight on the safety-first component is sufficiently large. Comparative statics analysis reveals that whether the optimal amount invested in the risky asset becomes smaller as the weight on the safety-first component increases depends on whether the safety wealth level is below the wealth obtained when the entire initial wealth is invested in the riskless asset. Further comparative statics analyses with respect to the safety wealth level and the degree of risk aversion in the expected utility component are also conducted. PubDate: 2022-06-01
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Abstract: Abstract The efficient market hypothesis is highly discussed in economic literature. In its strongest form, it states that there are no price trends. When weakening the non-trending assumption to arbitrary short, small, and fully unknown trends, we mathematically prove for a specific class of control-based trading strategies positive expected gains. These strategies are model free, i.e., a trader neither has to think about predictable patterns nor has to estimate market parameters such as the trend’s sign like momentum traders have to do. That means, since the trader does not have to know any trend, even trends too small to find are enough to beat the market. Adjustments for risk and comparisons with buy-and-hold strategies do not satisfactorily solve the problem. In detail, we generalize results from the literature on control-based trading strategies to market settings without specific model assumptions, but with time-varying parameters in discrete and continuous time. We give closed-form formulae for the expected gain as well as the gain’s variance and generalize control-based trading rules to a setting where older information counts less. In addition, we perform an exemplary backtesting study taking transaction costs and bid-ask spreads into account and still observe—on average—positive gains. PubDate: 2022-06-01
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Abstract: Abstract We provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox–Ross–Rubinstein (CRR) pricing model. The main tool used in this paper for simplifying the reasoning is applying static hedging arguments. In applying the static hedging principle, we consider Arrow–Debreu securities and digital options, or backward random processes. In the last case, the CRR model is extended to an infinite state space which leads to an interesting new phenomenon not present in the classical CRR model. At the end, we discuss the paradox involving the drift parameter \(\mu \) in the Black–Scholes–Merton model pricing. We provide sensitivity analysis and an approximation of the speed of convergence for the asymptotically vanishing effect of drift in prices. PubDate: 2022-06-01
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Abstract: Abstract In this article, we present a new class of pricing models that extend the application of Wishart processes to the so-called stochastic local volatility (or hybrid) pricing paradigm. This approach combines the advantages of local and stochastic volatility models. Despite the growing interest on the topic, however, it seems that no particular attention has been paid to the use of multidimensional specifications for the stochastic volatility component. Our work tries to fill the gap: we introduce two hybrid models in which the stochastic volatility dynamics is described by means of a Wishart process. The proposed parametrizations not only preserve the desirable features of existing Wishart-based models but significantly enhance the ability of reproducing market prices of vanilla options. PubDate: 2022-06-01
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Abstract: Abstract We are interested in problems related to forward starting options for Hull–White stochastic volatility model. Our objective is to obtain analytical, semi-analytical, or approximated expressions of its price for simulation. To obtain an analytical representation of the price, we use Yor’s formula. However, the analytical formula is difficult to implement. Next we consider semi-analytical expressions for the price. In order to have them, we use the tower property for conditional expectations with a certain filtration and explicitly calculate it. Then, we consider an expansion expression for the price using the semi-analytical expression to have a simple expression. The semi-analytical expressions and the expansion expression can reduce computational costs and standard errors when the Monte Carlo method is used. Finally, some numerical results are given to show their accuracy and efficiency. PubDate: 2022-06-01
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Abstract: Abstract This paper examines the competitive firm that has to make its production and hedging decisions under correlated price and background risks. The background risk can be either financial or non-financial, which is accommodated by using a bivariate utility function. The separation theorem is shown to hold in that the firm’s optimal output level depends neither on the firm’s bivariate utility function nor on the joint distribution of the price and background risks. We derive necessary and sufficient conditions under which the firm optimally opts for an over-hedge (under-hedge). We further derive necessary and sufficient conditions under which hedging has positive (negative) effect on the firm’s optimal output level. These conditions are shown to be related to the concept of expectation dependence and bivariate preferences that include correlation aversion (correlation loving) and cross-prudence (cross-imprudence). PubDate: 2022-06-01
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Abstract: Abstract In this article, we extend the framework of monetary risk measures for stochastic processes to account for heavy tailed distributions of random cash flows evolving over a fixed trading horizon. To this end, we transfer the \(L^p\) -duality underlying the representation of monetary risk measures to a more flexible Orlicz duality, in spaces of stochastic processes modelling random future evolution of financial values in continuous time over a finite horizon. This contributes, on the one hand, to the theory of real-valued monetary risk measures for processes and, on the other hand, supports a new representation of acceptability indices of financial performance. PubDate: 2022-06-01
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Abstract: Abstract Using a large dataset on major FX rates, we test the robustness of the rough fractional volatility model over different time scales, by including smoothing and measurement errors into the analysis. Our findings lead to new stylized facts in the log–log plots of the second moments of realized variance increments against lag which exhibit some convexity in addition to the roughness and stationarity of the volatility. The very low perceived Hurst exponents at small scales are consistent with the rough framework, while the higher perceived Hurst exponents for larger scales lead to a nonlinear behaviour of the log–log plot that has not been described by models introduced so far. PubDate: 2022-06-01
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Abstract: Abstract This paper demonstrates that endogenous fluctuations are possible in the market for loans. In the context of a three-period overlapping generations economy, the deposit rates offered to lenders are found to exhibit complex dynamics when financial intermediaries mediate borrowing and lending. Constant relative risk aversion of savers is found to generate a first-order nonlinear equation in the deposit rates. Concavity and convexity assumptions of production and savings functions are found to generate a type of dynamic relationship between the loan rates that is well known in the literature for generating complex dynamics. While the main analysis is conducted with general functions, an example is provided to support the theory presented. PubDate: 2022-06-01
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Abstract: Abstract The simplest and most natural vol-of-vol estimator, the pre-estimated spot variance-based realized variance, is typically plagued by a large finite-sample bias. In this paper, we analytically show that allowing for the overlap of consecutive local windows to pre-estimate the spot variance may correct for this bias. In particular, we provide a feasible rule for the bias-optimal selection of the length of local windows when the volatility is a CKLS process. The effectiveness of this rule for practical applications is supported by numerical and empirical analyses. PubDate: 2022-06-01
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Abstract: Abstract We calibrate a novel multifactor stochastic volatility model that includes as special cases the Heston-based model of De Col et al. (J Bank Finance 37(10):3799–3818, 2013) and the 3/2-based model of Baldeaux et al. (J Bank Finance 53:34–48, 2015). Using a dataset on vanilla option quotes in a triangle of currencies, we find that the risk neutral approach typically fails for the calibrated model, in line with the results of Baldeaux et al. (2015). PubDate: 2022-06-01
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Abstract: Abstract In a market where a stochastic interest rate component characterizes asset dynamics, we propose a flexible lattice framework to evaluate and manage options on equities paying discrete dividends and variable annuities presenting some provisions, like a guaranteed minimum withdrawal benefit. The framework is flexible in that it allows to combine financial and demographic risk, to embed in the contract early exercise features, and to choose the dynamics for interest rates and traded assets. A computational problem arises when each dividend (when valuing an option) or withdrawal (when valuing a variable annuity) is paid, because the lattice lacks its recombining structure. The proposed model overcomes this problem associating with each node of the lattice a set of representative values of the underlying asset (when valuing an option) or of the personal subaccount (when valuing a variable annuity) chosen among all the possible ones realized at that node. Extensive numerical experiments confirm the model accuracy and efficiency. PubDate: 2022-05-27 DOI: 10.1007/s10203-022-00371-0
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Abstract: Abstract Financial performance evaluation is intimately linked to risk measurement methodologies. There exists a well-developed literature on axiomatic and operational characterization of measures of performance. Hinged on the duality between coherent risk measures and reward associated with investment strategies, we investigate representation of acceptability indices of performance using expectile-based risk measures that recently attracted a lot of attention inside the financial and actuarial community. We propose two purely expectile-based performance ratios other than the classical gain-loss ratio and the Omega ratio. We complement our analysis with elicitability of expectile-based acceptability indices and their conditional version accounting for new information flow. PubDate: 2022-05-19 DOI: 10.1007/s10203-022-00369-8
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Abstract: Abstract This paper draws a parallel between the economic and financial points of view in the modeling of long-term yield curves and provides new results on asymptotic long rates. The Ramsey rule, which is the reference equation in the economic literature to compute long-term discount rates, links endogenous discount rate and marginal utility of aggregate optimal consumption at equilibrium. This paper proposes a unified framework and a financial interpretation of the economic discount rate given by the Ramsey rule, using marginal utility indifference prices for non-replicable zero-coupon bonds. Optimal discounted pricing kernel is at the core of this unifying approach and is determined through an optimization program that can be posed backward or forward. The dynamics and the long-term behavior of the marginal utility yield curve is studied in both settings. Special attention is paid to its dependency on the initial wealth of the economy, as well as on the time-horizon in the backward setting, extending previous results in the literature. PubDate: 2022-05-19 DOI: 10.1007/s10203-022-00370-1
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Abstract: Abstract The study applies the grey model (GM(1,1)) to the Verhulst differential equation for forecasting the Bitcoin transaction counts. The grey Verhulst model (GVM) is based on the data set of Bitcoin as recorded along 10 years from the 1st August 2010. The model accuracy is checked by the mean absolute percentage error (MAPE), while the model predictability is assessed by analysing a plot of the Verhulst model constructed upon the parameters provided by the GVM. The MAPE criterion suggests the reasonable accuracy of the overall GVM forecasting values and high accuracy by considering the last 400 forecasting values. Furthermore, the Verhulst model plot suggests that the GVM is potential on predictability as the plot is not chaotic. The GVM forecasting values suggest a slight future decline in transacting Bitcoin; this may be due to its competition with the other emerging cryptocurrencies. The GVM suggests a relatively high performance as compared to the usual one-variable forecasting model GM(1,1). PubDate: 2022-05-04 DOI: 10.1007/s10203-022-00368-9
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Abstract: Abstract In this paper, we study a class of markets, among which we can mention agricultural and energy markets, characterized by seasonality, i.e., in which demand and/or supply conditions cyclically alternate with a precise and known periodicity. We propose a new theoretical framework based on a cobweb model with adaptive expectations, accordingly modified to be consistent with market’s seasonality. The model, consisting in a second-order non-autonomous difference equation, is investigated with the aim of understanding how the periodical nature of the market together with the agents’ expectation formation mechanism affects the resulting dynamics. We analytically prove the emergence of dynamical scenarios that are missing in the classic cobweb model for non-seasonal markets, such as quasi-periodic dynamics and an ambiguous role on stability of the expectation weight. Finally, we discuss their economic rationale with the help of numerical simulations. In such a peculiar economic framework, agents’ learning plays a key role to explain the dynamical properties of economic observables. PubDate: 2021-12-01 DOI: 10.1007/s10203-021-00335-w
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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
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