Decisions in Economics and Finance

Gnoatto, Alessandro; Grasselli, Martino; Platen, Eckhard

doi: 10.1007/s10203-021-00330-1pmid: N/A

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).

Kountzakis, Christos E.; Rossello, Damiano

doi: 10.1007/s10203-021-00334-xpmid: N/A

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 Lp\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^p$$\end{document}-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.

Talponen, Jarno; Turunen, Minna

doi: 10.1007/s10203-021-00338-7pmid: N/A

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 μ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mu $$\end{document} 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.

Mukherji, Nivedita

doi: 10.1007/s10203-021-00341-ypmid: N/A

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.

Hata, Hiroaki; Liu, Nien-Lin; Yasuda, Kazuhiro

doi: 10.1007/s10203-021-00343-wpmid: N/A

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.

Toscano, Giacomo; Recchioni, Maria Cristina

doi: 10.1007/s10203-021-00349-4pmid: N/A

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.

Jansen, Dennis W.; Liu, Liqun

doi: 10.1007/s10203-021-00347-6pmid: N/A

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.

La Bua, Gaetano; Marazzina, Daniele

doi: 10.1007/s10203-021-00357-4pmid: N/A

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.

Wong, Kit Pong

doi: 10.1007/s10203-021-00362-7pmid: N/A

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).

Garcin, Matthieu; Grasselli, Martino

doi: 10.1007/s10203-021-00358-3pmid: N/A

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.