
on Risk Management 
By:  Irina Penner (CEREMADE); Anthony Reveillac (CEREMADE) 
Abstract:  The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for bounded \cd processes, we show that this framework provides a systematic approach to the both issues of model ambiguity, and uncertainty about the time value of money. We also establish a link between risk measures for processes and BSDEs. 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1304.4853&r=rmg 
By:  Yashkir, Olga; Yashkir, Yuriy 
Abstract:  In this study we investigated several most popular Loss Given Default (LGD) models (LSM, Tobit, ThreeTiered Tobit, Beta Regression, Inflated Beta Regression, Censored Gamma Regression) in order to compare their performance. We show that for a given input data set, the quality of the model calibration depends mainly on the proper choice (and availability) of explanatory variables (model factors), but not on the fitting model. Model factors were chosen based on the amplitude of their correlation with historical LGDs of the calibration data set. Numerical values of nonquantitative parameters (industry, ranking, type of collateral) were introduced as their LGD average. We show that different debt instruments depend on different sets of model factors (from three factors for Revolving Credit or for Subordinated Bonds to eight factors for Senior Secured Bonds). Calibration of LGD models using distressed business cycle periods provide better fit than data from total available time span. Calibration algorithms and details of their realization using the R statistical package are presented. We demonstrate how LGD models can be used for stress testing. The results of this study can be of use to risk managers concerned with the Basel accord compliance. 
Keywords:  LGD, Credit Risk, LGD model, Linear regression, Tobit model, Stress testing 
JEL:  G14 G17 G19 G24 
Date:  2013–03–27 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:46147&r=rmg 
By:  Mensi, Walid; Beljid, Makram; Boubaker, Adel; Managi, Shunsuke 
Abstract:  This paper employs a VARGARCH model to investigate the return links and volatility transmission between the S&P 500 and commodity price indices for energy, food, gold and beverages over the turbulent period from 20002011. Understanding the price behavior of commodity prices and the volatility transmission mechanism between these markets and the stock exchanges are crucial for each participant, including governments, traders, portfolio managers, consumers, and producers. For return and volatility spillover, the results show significant transmission among the S&P 500 and commodity markets. The past shocks and volatility of the S&P 500 strongly influenced the oil and gold markets. This study finds that the highest conditional correlations are between the S&P 500 and gold index and the S&P 500 and WTI index. We also analyze the optimal weights and hedge ratios for commodities/S&P 500 portfolio holdings using the estimates for each index. Overall, our findings illustrate several important implications for portfolio hedgers for making optimal portfolio allocations, engaging in risk management and forecasting future volatility in equity and commodity markets. 
Keywords:  Stock markets, Commodity prices, Volatility spillovers, Hedge ratios, VARGARCH models, Energy price 
JEL:  Q34 Q41 
Date:  2013–02–15 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:44395&r=rmg 
By:  Youssef ElKhatib; Abdulnasser HatemiJ 
Abstract:  Option pricing is an integral part of modern financial risk management. The wellknown Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the unconditional volatility of the original asset is increasing during a certain period of time. We consider a market suffering from a financial crisis. We provide the solution for the equation of the underlying asset price as well as finding the hedging strategy. In addition, a closed formula of the pricing problem is proved for a particular case. The suggested formulas are expected to make the valuation of options and the underlying hedging strategies during financial crisis more precise. 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1304.4688&r=rmg 
By:  Yannis G. Yatracos 
Abstract:  A statistical decision problem is hidden in the core of option pricing. A simple form for the price C of a European call option is obtained via the minimum Bayes risk, R_B, of a 2parameter estimation problem, thus justifying calling C Bayes (B)price. The result provides new insight in option pricing, among others obtaining C for some stockprice models using the underlying probability instead of the risk neutral probability and giving R_B an economic interpretation. When logarithmic stock prices follow Brownian motion, discrete normal mixture and hyperbolic Levy motion the obtained Bprices are "fair" prices. A new expression for the price of American call option is also obtained and statistical modeling of R_B can be used when pricing European and American call options. 
Date:  2013–04 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1304.5156&r=rmg 