International Journal of Financial Engineering

In this paper, the transition joint probability density function of the solution of geometric Brownian motion (GBM) equation is obtained via Lie group theory of differential equations (DEs). Lie symmetry analysis is applied to find new solutions for time-fractional Fokker–Planck–Kolmogorov equation of GBM. This analysis classifies the forms of the solutions for the equation by the similarity variables arising from the symmetry operators. Finally, an analytic method called invariant subspace method is applied in order to find another exact solution.

This paper proposes a model based on probability density functions associated with dynamics of underlying asset prices to measure contagion-induced systemic risk in the market. The two new risk measures with closed-form formulas derived from the model are (1) the rate of change of the probability of triggering a shock determined by the joint dynamics of prices of systemically important assets/entities and less important ones and (2) the distress correlation between the two types of assets/entities, which can provide forward-looking signals of such risk. The model is applied to the euro-area sovereign debt crisis and demonstrates how systemic liquidity shocks can build up in the sovereign debt market due to contagion between sovereign risk of small countries (i.e., Portugal) and systemically important countries (i.e., Italy and Spain). A signal of the rate of change of the joint probability appeared in April 2011 before the systemic liquidity shock occurred in November 2011. There exist endogenous critical levels of sovereign spreads, above which the signal materializes.

This paper discusses about the latest and efficient financial tools and techniques which optimize the financial cost of the organization and predict the financial situation of the organization to flourish the business in the efficient way. Financial management basically means to accumulate funding for the enterprise at a low cost and to expend this collected funding for earning extreme profits. Thus, financial management means to plan and control the finance of the company. Financial management is usually concerned with the flow and control of money within an organization and be it either reserved or open sector. So, these tools if functional in the better way then business will reach in the utmost altitude. Recently some computational tools have been developed by the computer scientist for the efficient management and prediction for the business which is very useful for forecast and prediction in the era of digital world. The intention of this paper is to review and discuss the most significant applications of Business Intelligence in financial management and forecasting and prediction domain as well as point to new technology trends that will affect financial development.

The adoption of explicit deposit insurance increases the moral hazard of banks’ risk-taking, caused by the decrease in depositors’ discipline. Based on the contract theory, this study probes whether the inception of risk-based deposit insurance premium may limit the moral hazard of banks’ risk-taking triggered by the deposit insurance. This study conducted the analysis on 2,196 banks of 125 countries, covered by the Bankscope database from 2002 to 2014 period. The hierarchical linear models (HLM) were used for empirical estimation of research models. The findings revealed that risk-based deposit insurance premium deteriorated the moral hazard of banks’ risk-taking, incited by the enactment of explicit deposit insurance, while this effect was high for the small banks. Therefore, the small banks were more stable and positively affected by the selection of risk-based deposit insurance premium as compared to the larger counterparts. However, it cannot eliminate this negative effect completely. Hence, the implementation of the premium structure by policymakers on the finding of this study encouraged the depositors and investors’ confidence in the banking system around the globe.

The study on the multiple-curve interest rate models becomes increasingly active since the 2007 credit crunch, for which one curve, typically the OIS curve, is used for discounting purpose, while the LIBOR curves (associated with various market tenors) are used for projecting the future cash flows. In this work, we extend the standard LIBOR market model to accommodate such multiple-curve setting by means of a multiplicative basis. The multiplicative basis is modeled as an exponential function of multi-factor square-root processes. Under the multiplicative basis setup, the OIS forward rates are correlated with the implied (additive) LIBOR-OIS spreads. We then derive closed-form pricing formulas for caplet, swaption, and interest rate futures in the multiplicative basis framework. In particular, we show that the valuation of caplet and swaption can be easily computed by a proper integral of real-valued functions, which facilitates the calibration of our model. Finally, we discuss a slight modification of our model to allow for negative interest rates.

In this paper we introduce the CHEB method, a quadrature-based methodology for the fast and accurate pricing of European options with arbitrary payoffs. The method comes as a natural application of Chebfun, a numerical computing software package built on the approximation properties of Chebyshev series and Chebyshev interpolants. For the methodology to be useful for practical purposes, we address two considerations: the recovery of the underlying’s density from the characteristic function, and the estimation of the truncation error. The methodology can be viewed as an extension of the COS method, a quadrature-based methodology designed for the pricing of standard, non-arbitrary payoffs.

In this paper, we study the deviation probability estimate for a leveraged exchanged-traded fund (LETF). By large deviation principle, we derive explicitly the logarithmic limit of the tail probability when the price of a LETF exceeds a given reference asset, which allows us to compute the underlying leverage ratio. Then we apply our results to various existing models, including the geometric Brownian motion (GBM) model, generalized autoregressive conditional heteroskedasticity (GARCH) model, inverse GARCH model, extended Cox–Ingersoll–Ross (CIR) model, 3/2 model, as well as the Heston and 3/2 stochastic volatility models, and to present their corresponding optimal leverage ratios, respectively.

Most reported stochastic volatility (SV) model for interest rates only deals with an AR specification for the latent factor process. We show in this paper the technical details for specifying the SV model for interest rates that includes an ARMA structure, a jump component and additional exogenous variables for the latent factor process. We demonstrate the efficacy of this approach with an application to the US short-term interest rate data. We find that the elasticity parameter of the variance is closer to 0.5, i.e., similar to that of the Cox–Ingersoll–Ross (1985) model of interest rates. This is quite a contrast to the finding Chan et al. [Chan, KC, GA Karolyi, F Longstaff and A Sanders (1992). The volatility of short-term interest rates: An empirical comparison of alternative models of term structure of interest rates, Journal of Finance, 47, 1209–1227]. who found the elasticity to be close to 1.5.

In this paper, we propose a Fenchel duality approach to study the minimization problem of the shortfall risk. We consider a general increasing and strictly convex loss function, which may be more general than the situation of convex risk measures usually assumed in the literature. We first translate the associated stochastic optimization problem to an equivalent static optimization problem, and then obtain the explicit structure of the optimal randomized test for both complete and incomplete markets. For the incomplete market case, to the best of our knowledge, we obtain for the first time the explicit randomized test, while previous literature only established the existence through the supermartingale optional decomposition approach. We also solve the shortfall risk minimization problem for an insider through the enlargement of filtrations approach.

We propose a new methodology to evaluate VIX derivatives. The approach is based on a closed-form Hermite series expansion, and can be applied to general stochastic volatility models. We exemplify the proposed method using the Heston model, the mean-reverting CEV model and the 3/2 model. Numerical results show that the proposed method is accurate and efficient.