CEV model equipped with the long-memory Fallah, Somayeh; Mehrdoust, Farshid
Journal of computational and applied mathematics,
June 2021, 2021-06-00, Volume:
389
Journal Article
Peer reviewed
In this paper, we define the mixed fractional Constant Elasticity of Variance (CEV) process exploiting a transfer equation. This transformation enables us to shift non-linearity from the volatility ...coefficient into the drift one and accordingly, the problem can be more easily studied. We confirm the existence of a unique positive solution to the transfer equation and verify the conditions under which the probability that, on any fixed finite interval, the mixed fractional CEV process does not hit zero tends to 1 (by some simulation, we illustrate more). Next, some parameters of the process are estimated and finally, we examine the ability of this process to model a financial market.
The pricing of option contracts when the underlying process follows the constant elasticity of variance (CEV) model is considered. For CEV European options, the closed-form solutions involve the ...non-central chi-square distribution, whose computations by the current literatures are rather unstable and extremely expensive. Based on multiquadric quasi-interpolation methods, this study suggests a stable and fast numerical algorithm for CEV option pricing model. The method is confirmed to be a multinomial tree, in which the underlying variable moves from its initial value to an infinity of possible values of the next time step. The probabilities in the associated tree are ensured to be positive, which is a sufficient condition for stability and convergence. The method is flexible, since it is simple to implement with the nonuniform knots. Moreover, the method is easy to value the Greek letters which are important parameters in financial engineering, as the multiquadric function is infinitely continuously differentiable. Besides, the method does not require solving a resultant full matrix, the ill-conditioning problem arising when using the radial basis functions as a global interpolant can be avoided. Numerical experiments imply that the method is highly effective to calculate the stock options and its Greeks under the CEV model.
The continuous observation of the financial markets has identified some ‘stylized facts’ which challenge the conventional assumptions, promoting the born of new approaches. On the one hand, the ...long-range dependence has been faced replacing the traditional Gauss–Wiener process (Brownian motion), characterized by stationary independent increments, by a fractional version. On the other hand, the CEV model addresses the Leverage effect and smile-skew phenomena, efficiently. In this paper, these two insights are merging and both the fractional and mixed-fractional extensions for the CEV model, are developed. Using the fractional versions of both the Itô’s calculus and the Fokker–Planck equation, the transition probability density function of the asset price is obtained as the solution of a non-stationary Feller process with time-varying coefficients, getting an analytical valuation formula for a European Call option. Besides, the Greeks are computed and compared with the standard case.
In this paper, we consider the optimal investment problem for both an insurer and a reinsurer. The insurer’s wealth process is described by a jump diffusion risk model and the insurer can purchase ...proportional reinsurance from the reinsurer. Both the insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset whose price process follows the constant elasticity of variance (CEV) model. Moreover, the correlation between risk model and the risky asset’s price is considered. The objective is maximizing the expected utility of the insurer’s and the reinsurer’s terminal wealth. Applying stochastic control theory, we establish the corresponding Hamilton–Jacobi–Bellman (HJB) equations and derive optimal investment–reinsurance strategies for exponential utility function. Finally, numerical examples are provided to analyze the effects of parameters on the optimal strategies.
Viperin, also known as radical S-Adenosyl methionine domain containing 2 (RSAD2), is an IFN stimulated protein that plays crucial roles in innate immunity. Here, we identified a viperin gene from the ...koi carp (Cyprinus carpio) (kVip). The ORF of kVip is 1047 bp in length, encoding a polypeptide of 348 amino acids with neither signal peptide nor transmembrane protein. The predicted molecular weight is 40.37 kDa and the isoelectric point is 7.7. Multiple sequence alignment indicated that putative kVip contains a radical SAM superfamily domain and a conserved C-terminal region. kVip was highly expressed in the skin and spleen of healthy koi carps, and significantly stimulated in both natural and artificial CEV-infected koi carps. In vitro immune stimulation analysis showed that both extracellular and intracellular poly (I: C) or poly (dA: dT) caused a significant increase in kVip expression of spleen cells. Furthermore, intraperitoneal injection of recombinant kVip (rkVip) not only reduced the CEV load in the gills, but also improved the survival of koi carps following CEV challenge. Additionally, rkVip administration effectively regulated inflammatory and anti-inflammatory cytokines (IL-6, IL-1β, TNF-α, IL-10) and interferon-related molecules (cGAS, STING, MyD88, IFN-γ, IFN-α, IRF3 and IRF9). Collectively, kVip effectively responded to CEV infection and exerted antiviral function against CEV partially by regulation of inflammatory and interferon responses.
•kVip was identified in koi carp, and its expression was highest in the skin and spleen, followed by the blood and gills.•KVip was markedly induced in immune organs by both natural and artificial CEV infection.•Extracellular and intracellular poly(I:C) or poly (dA:dT) caused a significant increase in kVip expression in spleen cells.•rkVip not only reduced the CEV copies in gills, but also improved the survival rate of koi carps against CEV infection.•rkVip effectively regulated the inflammatory cytokines and interferon-related molecules of koi carps following CEV infection.
We study a defined contribution pension system with the return of premium clauses, which is embedded with two administrative fees: the charge on balance and the charge on flow. The fund wealth is ...invested in financial market with a riskless asset and a risky asset modeled by a constant elasticity of variance process. We use the Weibull model to characterize the force of mortality. The dynamic programming principle is applied to derive optimal investment strategies explicitly when the pension member has constant absolute risk aversion and constant relative risk aversion. We illustrate how the certainty equivalent of the expected utility works for comparing the two fees. Finally, we give a numerical analysis to highlight our results.
•Optimal investment strategies are derived for the DC plan mathematically.•The effects of two administrative fees on optimal investment are analyzed.•The Weibull model is used to describe the force of mortality.•CARA and CRRA utilities are chosen for the pension member.•The comparison method of the two fees is provided.
An outbreak of a carp disease occurred in a koi pond in early October 2016, Chengdu, southwest of China. Characteristic signs of infected fish include erratic swimming of moribund fish at the water ...surface, respiratory distress, presence of thick and foggy mucus covering the body and gills. Skin ulcers were also noticed in a few cases. Microbiological, parasitological and virological investigations were carried out with fish samples collected from various localities. Histologically, the gills, kidney and liver showed discernible changes. By analyzing gill tissues in six samples by PCR and nested-PCR for detection of cyprinid herpesvirus 3 (CyHV-3) and carp edema virus (CEV) respectively, PCR products of 292 bp and 478 bp (by using nested primers) could be amplified. The outbreak of carp disease caused by CEV and CyHV-3 mixed infection was confirmed by sequence analysis of the PCR products. The viral load in the gills and kidney were quantified by real-time TaqMan PCR, which in turn would aid the evaluation of the significance of the virus to the etiology of the disease. The result demonstrated that CEV plays the major role to the death of fish. Phylogenetic analyses revealed that the CEV isolate (GenBank accession no. MG189371) showed closest identity to the CEV isolated from UK (KX254027) with 99% homology. To our knowledge, this is the first report a carp disease caused by CEV and CyHV-3 mixed infection in China.
•A carp disease caused by CEV and CyHV-3 mixed infection.•An outbreak of carp disease occurred in a koi pond in southwest of China.•CEV was the major virus to cause the death.
In the equity markets the stock price volatility increases as the stock price declines. The classical Black–Scholes–Merton (BSM) option pricing model does not reconcile with this association. Cox ...introduced the constant elasticity of variance (CEV) model in 1975, in order to capture this inverse relationship between the stock price and its volatility. An important parameter in the model is the parameter β, the elasticity of volatility. The CEV model subsumes some of the previous option pricing models. For β=0, β=−1∕2, and β=−1 the CEV model reduces respectively to the BSM model, the square-root model of Cox and Ross, and the Bachelier model. Both in the case of the BSM model and in the case of the CEV model it has become traditional to begin a discussion of option pricing by starting with the vanilla European calls and puts. However, there are simpler solutions to both models than those pertaining to the standard calls and puts. Mathematically, it makes sense to investigate the simpler cases first. In the case of BSM model simpler solutions are the log and power solutions. Similar simple solutions have not been studied so far for the CEV model. We use a group-theoretic method, Kovacic’s algorithm, which has not been used before to problems of Finance or Economics and obtain new classes of elementary function solutions to the CEV model for all half-integer values of β. In particular, when β=⋯,−52,−2,−32,−1,1,32,2,52,…, we obtain four new classes of denumerably infinite elementary function solutions, when β=−12 and β=12 we obtain two new classes of denumerably infinite elementary function solutions, whereas, when β=0 we find two elementary function solutions.
This paper offers novel analytical solutions for evaluating perpetual caps and floors on continuous flows under the constant elasticity of variance (CEV) model. We demonstrate that the inclusion of a ...perpetual bubble value is required to avoid arbitrage opportunities in the case of the CEV process with upward-sloping volatility skews. We then extend the previous literature on caps and floors arrangements by providing new analytical formulae for valuing finite maturity caps and floors that are contingent on continuous flows. We discuss the impact of the finite-lived solutions on the optimal behavior of a firm, relative to the perpetual case. We also show the implications of the correct specification of the underlying state variable process for the valuation of caps and floors by comparing the CEV results with the ones obtained when assuming a lognormal diffusion. Practical applications of these contractual agreements arising within the context of executive management decisions are also discussed.
•Perpetual caps and floors on continuous flows under the CEV process.•Finite maturity caps and floors on continuous flows under the CEV process.•Feed-in tariff contracts under the CEV process.•Applications in the context of executive management decisions.
PDF
