International Journal of Financial Engineering

This study attempts primarily to measure the financial performance of banking industry of Bangladesh for the periods 2013–2014 and to rate them according to the composite rating system. For this purpose, 10 private commercial banks (PCBs) have been selected from 38 PCBs. CAMEL has critically analyzed the financial performance of these banks. This finds that most of the banks get 2.14 with an average rating of composite range, where only Eastern Bank Ltd. gets “Strong” rating, seven PCBs get “Satisfactory” rating, AB Bank Ltd. and City Bank Ltd. lay middle of the range of composite score. From this ground, it is clearly reflected that most of the PCBs in Bangladesh have performed quite satisfactorily in recent years. The performance of most banks is dependent more on the managerial ability in formulating strategic plans and the efficient implementation of its strategies. Maintenance of asset quality is the major challenge in this year and is feared to remain so in 2014. The banking sector in Bangladesh has passed somewhat an average year regarding governance, profitability and soundness in 2013. Finally, it is recommended that the banks should be more careful to ensure the quality of assets and its uses, and increased their efficiency in managerial grids.

This paper provides a thorough survey of the European option pricing, with new trends in the risk measurement, under exponential Lévy models. We develop all steps of pricing from equivalent martingale measures construction to numerical valuation of the option price under these measures. We then construct an algorithm, based on Rockafellar and Uryasev representation and fast Fourier transform, to compute Risk indicators, like the VaR and the CVaR of derivatives. The results are illustrated with an example of each exponential Lévy class. The main contribution of this paper is to build a comprehensive study from the theoretical point of view to practical numerical illustration and to give a complete characterization of the studied equivalent martingale measures by discussing their similarity and their applicability in practice. Furthermore, this work proposes applications to the Fourier inversion technique in risk measurement.

A spread option is a contingent claim whose underlying is the price difference between two assets. For a call, the holder of the option receives the difference, if positive, between the price difference and the strike price. Otherwise, the holder receives nothing. Spread options trade in large volume in financial, fixed-income, commodity, and energy industries. It is well known that pricing of spread options does not admit closed-form solutions even under a geometric Brownian motion paradigm. When price dynamics experience stochastic volatilities and/or jumps, the valuation process becomes more challenging. Following the seminal work of Jarrow and Judd, we propose the use of Edgeworth expansion to approximate the call price. In the spirit of Pearson, we reduce the cumbersome computation inherent in Edgeworth expansion to single numerical integrations. For an arbitrary bivariate price process, we show that once its product cumulants are available, either by virtue of the structural properties of the underlying processes or by empirical estimation using market data, the approach enables analysts to approximate the call price easily. Specifically, the call prices so estimated capture the correlation, skewness, and kurtosis of the two underlying price processes. As such, the approach is useful for approximate valuations based on Lévy-based models.

We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process. Rigorous accuracy results are provided for European-style claims. For barrier-style claims, we include several numerical examples to illustrate the accuracy and versatility of our approximations.

We consider the valuation of collateralized derivative contracts such as bond option or Caplet contracts. We allow for posting different collaterals such as securities or cash for the derivatives and its hedges. The pricing is based on modeling the joint evolution of collateral rate and the spread between collaterals. The Hull–White models are applied to collateral rate and spread to generate the closed pricing formula for zero coupon bond option. We also derive the pricing formula for Caplet under the Libor Market model and SABR model framework.

We study the optimal execution of market and limit orders with permanent and temporary price impacts as well as uncertainty in the filling of limit orders. Our continuous-time model incorporates a trade speed limiter and a trade director to provide better control on the trading rates. We formulate a stochastic control problem to determine the optimal dynamic strategy for trade execution, with a quadratic terminal penalty to ensure complete liquidation. In addition, we identify conditions on the model parameters to ensure optimality of the controls and finiteness of the associated value functions. For comparison, we also solve the schedule-following optimal execution problem that penalizes deviations from an order schedule. Numerical results are provided to illustrate the optimal market and limit orders over time.

We consider a portfolio consisting of a risk-free bond and an equity index which follows a jump diffusion process. Parameters for the inflation-adjusted return of the stock index and the risk-free bond are determined by examining 89 years of data. The optimal dynamic asset allocation strategy for a long-term pre-commitment mean variance (MV) investor is determined by numerically solving a Hamilton–Jacobi–Bellman partial integro-differential equation. The MV strategy is mathematically equivalent to minimizing the quadratic shortfall of the target terminal wealth. We incorporate realistic constraints on the strategy: discrete rebalancing (yearly), maximum leverage, and no trading if insolvent. Extensive synthetic market tests and resampled backtests of historical data indicate that the multi-period MV strategy achieves approximately the same expected terminal wealth as a constant weight strategy, but with much smaller variance and probability of shortfall.

This paper studies the empirical facts of agency mortgage-backed securities price dynamics. Based on an explicit formula for MBS pricing developed in this paper, the prepayment rate can be implied from the market price. The standard structural form approach calculates the prices from the structure of prepayments. We reverse the problem, deriving the prepayment from the price. We find that the price change does not necessarily reflect the change of actual prepayment. The explicit formula and calibration strategies developed in this paper provide an alternative way to analyze and valuate the MBS.

Option pricing under two stochastic volatility models, double Heston model and double Heston with three jumps, is done. Firstly, the efficiency of the second model is shown via FFT method, and numerical examples using power call options. Then it is shown that power option yields more premium income under the second model, double Heston with three jumps, than another one.

This paper primarily examines both causality effect of banks’ capital regulation and risk-taking behavior based on generalized methods of moment (GMM) for a dynamic unbalanced panel observation of 32 commercial banks in Bangladesh over the period 2000–2014. The empirical findings of this study suggest that capital regulation has a significant effect on risk-taking behavior, and excessive risks impede the growth of capital ratio as well as the stability. Moreover, from bank-level data, size does not uniformly affect the quantity of capital and risk. Large banks have poor capital ratio and higher inclination to risk than small size counterpart. Small size banks are well managed in capital ratio and risk-taking that glitter their stability through the periods. Besides these effects, corporate governance notably influenced banks to reduce credit risk and enhance stability. Finally, this paper provides some implications for the think tanks and stakeholders of the country.

This study investigates the effect of market competition and development indicators on bank risk-taking behavior, capital regulation, and efficiency of banks in Asian emerging economies in light of their recent financial liberalization. Using stochastic frontier analysis (SFA) for measuring cost and profit inefficiency and regressed simultaneous equations by following the approach of generalized methods of the moment (GMM) the study covers a sample of 191 banks for the period between 2000 and 2014 in three Asian emerging economies such as Bangladesh, China, and India. The robust empirical results of GMM panel estimator reveal three core findings: first, intense competition of Asian banks has a positive association with risk-taking but has a negative correlation with regulatory capital and inefficiency. Second, it provides evidence that in economic progression, sample banks having a strong tendency of taking the risk. But no significant relationship found between GDP growth and capital, and GDP growth and inefficiency. This paper thus provides compelling insights to the policy makers and bank managers in setting appropriate strategy for a financial institution in the region.

We propose a new class of models for pricing generalized variance swaps. We assume that, in the most general form, the process for the asset price is a function of a general time-homogeneous diffusion process belonging to a symmetric pricing semigroup, time changed by a composition of a Lévy subordinator and an absolutely continuous process. We derive the analytical pricing formulas for various types of generalized variance swaps based on eigenfunction expansion method. We also numerically implement the model and test its sensitivity to some of the key parameters of the model.

A new short-rate model and a new explicit instantaneous mean reversion formula are introduced. The introduction is presented via a comparison of various short-rate one factor models, which are calibrated and analyzed numerically via a Monte Carlo simulation. Two variance reduction techniques, Stratified Sampling and the Sobol Algorithm, are compared. An empirical comparison is constructed using criteria of goodness-of-fit, in five exchange rates. The data is ex-ante ultimately measuring the predictability of the stochastic models and variance reduction.

In this paper, we consider hedging and pricing of illiquid options on an untradable underlying asset, where an alternative asset is used as a hedging instrument. Particularly, we consider the situation where the trade price of the hedging instrument is subject to market impacts caused by the hedger and the liquidity costs paid as a spread from the mid price. Pricing illiquid options, which often appears in trading of structured products, is a critical issue in practice because of its difficulties in hedging mainly due to untradability of the underlying asset as well as the liquidity costs and market impacts of the hedging instrument. First, by setting the problem under a discrete time model, where the optimal hedging strategy is defined by the local risk-minimization, we present algorithms to obtain the option price along with the hedging strategy by an asymptotic expansion. Moreover, we provide numerical examples. This model enables the estimation of the effect of both the market impacts and the liquidity costs on option prices, which is important in practice.

This paper presents the Generalized Poisson Jump Process to describe the effect of radical technological innovation on the market. It defines the market impact index of radical technological innovation, and constructs a real option game model for radical technological innovation. Besides, this paper develops a numerical method in the model to show that the market impact index of radical technological innovation and the Generalized Poisson Process parameter both have a good influence on both the investment value and investment limit.

We introduce a closed form approximation for the implied volatility of ATM-forward options. The relative error of this approximation is uniformly bounded for all option maturities and implied volatilities. The approximation is extremely precise, having relative error less than $10^{-6}$ for all options with integrated volatility less than $1.9$, such as options with maturity less than three years and implied volatility less than 100%. Moreover, the approximate implied volatilities fall within the implied volatility bid–ask spread for all the liquid options, such as options with volatility less than 200% and maturity less than nine years.

This study presents an efficient method for pricing the American fractional lookback option in the case where the stock price follows a mixed jump diffusion fraction Brownian motion. By using It ô formula and Wick–It ô–Skorohod integral, a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

We provide the first formal investigation of the consequences of negative interest rates in the Eurozone on the pricing of interest rate options. Since the money market rates settled in negative territory and other market segments experienced negative yields, the broader financial community has had to face an unknown environment. The well-known Black–Scholes (BS) framework has become unfeasible for interest rate option valuation. First of all, no-arbitrage properties are breached, allowing arbitrage opportunities. More, the BS framework’s assumption of a log-normal distribution of the underlying rates does not stand with negative interest rates. We argue that the most notable approach which allows interest rate option pricing is [Bachelier, L (1900). Théorie de la speculation, 3rd Annales scientifiques de l’École Normale Supēérieure 17, 21–86.], which assumes a normal distribution of the underlying rates. We demonstrate that the Bachelier model represents an answer to the critical issues that are raised in our study. Still, we highlight that it is far from being an accurate pricing model. Our research aims to light up an intense debate about alternative solutions among academics, financial professionals and institutions, and policy makers.

Most small businesses face uncertain demand for their products and services. The revenue they earn is most likely to be of stochastic nature. They face difficulties in making a fixed loan repayment throughout the life of the loan as they earn stochastic revenues. If banks are to lend to this market using the fixed loan repayment schedule/regime, it is highly likely that these businesses will default on their repayments several times in period $n$. If default rate is high in a loan portfolio, it means that the bank has to set up a higher bad loan provision, thereby tying up its capital. This reduces the lending business, profitability and growth of the financial institution. This is one of the reasons why financial institutions perceive these small businesses as a high risk market. Only financial institutions with a very high risk appetite will tap into this market. We are proposing revenue-based lending as a solution to the problem. Stochastic repayments will reduce periodic defaults. This reduction in periodic defaults will reduce the bad loan provision thereby making more funds available for lending. We want to show that the bad loan provision for the bank will be higher for a fixed loan repayment compared to the stochastic loan repayment.

The paper builds an equilibrium model to analyze the effect of risk aversion, risk seeking and loss aversion on corporate financing choice, capital structure and price impact. It shows that if the probability of a gain is higher than a certain level, risk aversion parameter has a positive relation with capital structure and price impact; while risk seeking parameter has a negative relation with capital structure and price impact, and vice versa. Loss aversion has negative relation with capital structure and price impact. The numerical simulation verifies our findings to some extent.

This paper proposes a new approach to style analysis of mutual funds in a general state space framework with particle filtering and generalized simulated annealing (GSA). Specifically, we regard the exposure of each style index as a latent state variable in a state space model and employ a Monte Carlo filter as a particle filtering method, where GSA is effectively applied to estimating unknown parameters.

An empirical analysis using data of three Japanese equity mutual funds with six standard style indexes confirms the validity of our method. Moreover, we create fund-specific style indexes to further improve estimation in the analysis.

This paper introduced an analytical solution and improved one-factor Gaussian copula models to the pricing of tranches of a Collateralized debt obligations (CDO) portfolio. Prices of CDO tranches are calculated and compared using the analytical model and different one-factor Gaussian copula models including a two-category heterogeneous model and a completely heterogeneous model that uses individual rate parameter and correlation coefficient for each reference entity in a CDO portfolio. When correlation among reference entities is low, the price calculated from the analytical model matches very well with the one-factor Gaussian copula models. However, as the correlation among reference entities increases, prices calculated using both the analytical solution and the homogeneous or two-category one-factor Gaussian copula models significantly deviate from the completely heterogeneous one-factor Gaussian copula model. This result verifies our belief that uniform parameters cannot completely capture all the heterogeneities in a CDO portfolio. Completely heterogeneous one-factor Gaussian copula model using individual rate parameters and correlation coefficients for each reference entities provides more reliable and accurate prices for structured securities.