On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Bühlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.     

Consumption-based equity valuation

Using a CCAPM-based risk-adjustment model, we perform yearly valuations of a large sample of stocks listed on NYSE, AMEX, and NASDAQ over a 30-year period. The model differs from standard valuation models in the sense that it adjusts forecasted residual income for risk in the numerator rather than through a risk-adjusted cost of equity in the denominator. The risk adjustments are derived based on assumptions about the time-series properties of residual income returns and aggregate consumption rather than on historical stock returns. We compare the performance of the model with several implementations of standard valuation models, both in terms of median absolute valuation errors (MAVE) and in terms of excess returns on simple investment strategies based on the differences between model and market prices. The CCAPM-based valuation model yields a significantly lower MAVE than the best performing standard valuation model. Both types of models can identify investment strategies with subsequent excess returns. The CCAPM-based valuation model yields time-series of realized hedge returns with more and higher positive returns and fewer and less negative returns compared with the time-series of realized hedge returns based on the best performing standard valuation model for holding periods from 1 to 5 years. In a statistical test of 1-year-ahead excess return predictability based on the models’ implied pricing errors, the CCAPM-based valuation model is selected as the better model. Using the standard series of aggregate consumption and the nominal price index, a reasonable level of relative risk aversion, and calibrated growth rates in the continuing value at each valuation date, the CCAPM-based valuation model produces small risk adjustments to forecasted residual income and low continuing values. Compared with standard valuation models, it relies less on estimated parameters and speculative elements when aggregating residual earnings forecasts into a valuation.     

Geometric Asian option pricing in general affine stochastic volatility models with jumps

In this paper, we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process can be cast, and we shall obtain closed form solutions for some relevant affine model classes.     

Option pricing: A general equilibrium approach

This article examines option valuation in a general equilibrium framework. We focus on the general equilibrium implications of price dynamics for option valuation. The general equilibrium considerations allow us to derive an alternative option valuation formula that is as simple as the Black and Scholes formula, and that exhibits different behavior with respect to the exercise price and time to expiration. They also help us clarify comparative-statics properties of option valuation formulas in general and of the Black and Scholes model in particular.     

Equilibrium Valuation of Foreign Exchange Claims

This article studies the equilibrium valuation of foreign exchange contingent claims. Within a continuous-time Lucas (1982) two-country model, exchange rates, interest rates and, in particular, factor risk prices are all endogenously and jointly determined. This guarantees the internal consistency of these price processes with a general equilibrium. In the same model, closed-form valuation formulas are presented for currency options and currency futures options. Common to these formulas is that stochastic volatility and stochastic interest rates are admitted. Hedge ratios and other comparative statics are also provided analytically. It is shown that most existing currency option models are included as special cases.     

投资银行业经理人估值与分配机制研究——基于多层次的利益相关者分析框架

现阶段我国投资银行经理人的估值与薪酬考核面临如下困境:一方面由于某种错觉,社会普遍认为投行经理人的收入远远高于合理水平;但另一方面,经理人的实际薪酬水平与其他行业以及国外同行相比明显偏低,投行经理人的激励严重不足。立足于我国现有制度现实,应该寻找一种渐进的、与现有制度安排协调的投行经理人估值与分配模式。本文基于利益相关者分析框架考察了投行经理人的估值与分配机制,运用模型从环境分析、组织模式和方法体系三个递进的层次对经理人的业绩评价进行了系统分析,从理论上对我国投资银行经理人的估值模型进行了开拓性研究。     

Option pricing using a binomial model with random time steps (A formal model of gamma hedging)

This paper provides a new option pricing model which justifies the standard industry implementation of the Black-Scholes model. The standard industry implementation of the Black-Scholes model uses an implicit volatility, and it hedges both delta and gamma risk. This industry implementation is inconsistent with the theory underlying the derivation of the Black-Scholes model. We justify this implementation by showing that these adhoc adjustments to the Black-Scholes model provide a reasonable approximation to valuation and delta hedging in our new option pricing model.     

Inflation and the Constant Growth Model: Reconciling the Literature

We formulate a generalized constant growth valuation model incorporating inflation and capital maintenance. We find that in general there are two sources of growth: growth due to capital maintenance and growth due to net new investments. The generalized version of the constant growth model allows the reconciliation of the existing literature, particularly the works of Gordon and Shapiro (1956), Lally (1988), and Bradley and Jarrell (2008), which all employ particular definitions of capital maintenance. Evaluating the practical relevance of either model we find that each model is best suited for a very particular company set‐up, which does not necessarily correspond to the commonly observed business models. The generalized version of the constant growth valuation model, however, presents a flexible approach that is capable of capturing various conceptions of capital maintenance.     

A Synthesis of Equity Valuation Techniques and the Terminal Value Calculation for the Dividend Discount Model

This paper lays out alternative equity valuation models that involve forecasting for finite periods and shows how they are related to each other. It contrasts dividend discounting models, discounted cash flow models, and residual income models based on accrual accounting. It shows that some models that are apparently different yield the same valuation. It gives the general form of the terminal value calculation in these models and shows how this calculation serves to correct errors in the model. It also shows that all models can be interpreted as providing a particular specification of the terminal value for the dividend discount model. In so doing it shows how one calculates the terminal value for the dividend discount formula. The calculation involves weighting forecasted stocks and flows of value with weights determined by a parameter that can be discovered from pro forma analysis.     

Option Pricing Under Autoregressive Random Variance Models

Abstract

The autoregressive random variance (ARV) model introduced by Taylor (1980, 1982, 1986) is a popular version of stochastic volatility (SV) models and a discrete-time simplification of the continuous-time diffusion SV models. This paper introduces a valuation model for options under a discrete-time ARV model with general stock and volatility innovations. It employs the discretetime version of the Esscher transform to determine an equivalent martingale measure under an incomplete market. Various parametric cases of the ARV models, are considered, namely, the log-normal ARV models, the jump-type Poisson ARV models, and the gamma ARV models, and more explicit pricing formulas of a European call option under these parametric cases are provided. A Monte Carlo experiment for some parametric cases is also conducted.     

The Gap between the Theory and Practice of Corporate Valuation: Survey of European Experts

The valuation of companies or their assets is at the heart of most financing and investment decisions. Over the last five decades, academics have developed several simple and sophisticated models for corporate valuation. Yet valuation estimates of a firm or its assets appear to vary widely among practitioners. It is unclear whether these differences arise from practitioners' use of different valuation models or from differences in their assumptions about the inputs used in those models. To provide some insights into this issue, the authors recently surveyed 365 European finance practitioners with CFAs or equivalent professional degrees. They find that almost all survey respondents use the Discounted Cash Flow (DCF) model (along with some version of Relative Valuation that relies on the use of “comparables”). But the estimation methods of such practitioners for almost all inputs in the DCF model, including beta, the equity market risk premium, leverage, cost of debt, and terminal value, vary widely. This can be a serious problem because even small differences in inputs can cause huge variations in valuations. Such differences arise primarily because theory provides little guidance on how to estimate parameters, leaving practitioners to make their own assumptions and judgments. In sum, the authors' findings suggest that the process of estimating valuation parameters can be as important as the choice of the valuation model itself, and requires the serious attention of academics and practitioners. The authors recommend that key valuation parameter estimates be disclosed in financial and valuation reports. Their findings are also relevant to policy makers because the concept of “fair value” plays such a central role in post‐crisis regulation.     

The Challenge of Valuing Patents and Early-State Technologies

The enormous risk of commercializing inventions is not captured by standard valuation models and can cause their results to be wildly misleading. As a consequence, the valuation results seem irrelevant to managers and investors, and the models are not used in key business decisions. This article is about building relevant valuation models for patents and early-stage technologies.
The importance of valuing innovation goes beyond the details of dueling models. Numerous academic studies have placed innovation at the center of economic growth. Improved valuation models for patents and early-stage technologies can help to attract capital and facilitate transactions, thereby strengthening incentives for innovation.
As this review demonstrates, however, valuing patents and early-stage technologies is a difficult problem with no easy answer. One must choose and then customize a model to match the salient features of the application—and even then, the analysis will often provide at best a range of possible values. But even if quantitative real options models are likely to be of limited use in many cases, real options thinking has a major role to play in both "framing" the valuation and guiding the management of patents and early-stage technologies.     

基于会计信息的权益估值研究:线性信息动态过程视野

基于经典权益定价理论,我们给出了广义的线性信息动态过程下的权益价值定价方法,并将线性权益定价模型拓展到了更一般的基于p阶历史信息的情形。本研究为探讨会计信息与公司权益价值之间的关系提供了重要的理论基础。     

Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported.This paper represents the view of the author and does note necessarily the views of the Mitsubishi UFJ Securities Co., Ltd. or members of its staff.     

Pricing Commodity Spread Options with Stochastic Term Structure of Convenience Yields and Interest Rates

The purpose of this research is to provide a valuation formula for commodity spread options. Commodity spread options are options written on the difference of the prices (spread) of two commodities. From the aspect of commodity contingent claims, it is considered that commodity spread options are difficult to evaluate with accuracy because of the existence of the convenience yield. Hence, the model of the convenience yield is the key factor to price commodity spread options. We use the concept of future convenience yields to develop the model that enriches the stochastic behavior of convenience yield. We also introduce Heath-Jarrow-Morton interest rate model to the valuation framework. This general model not only captures the mean reverting feature of the convenience yield, but also allows us to handle a very wide range of shape that the term structure of convenience yield can take. Therefore our model provides various types of models. The numerical analysis presented in this paper provides some unique features of commodity spread options in contrast to normal options. These characteristics have never been addressed in previous studies. Moreover, it suggests that the existing model overprice commodity spread options through neglecting the effect of interest rates.     

新兴产业估值方法国际比较与实证

估值是定价的基础,新兴产业由于自身的特点,在估值和定价发行方面存在较大的困难。本文对新兴产业的估值与定价问题展开研究,对现在市场主流的估值方法进行了对比,结合新兴产业估值特点,在传统PEG模型基础上发展出风险调整PEG模型,也即PEGX。它比PEG指标更全面地反映新兴行业企业的成长性和风险性。文章结合国内外资本市场进行了案例分析,通过实证检验验证了模型的有效性,更适用于对我国的新兴产业进行估值。文章认为,可以通过与PE模型及其他绝对估值模型结合,使用该模型对新股上市定价的合理性进行评估。由于PEGX模型更加强调新兴产业的风险性,用该模型进行定价分析时,可以有效缓解对高增长企业给予盲目的高估值定价。     

Towards an understanding of profitability analysis within the residual income valuation framework

This paper argues that there is a mis-match between formal theoretical accounting valuation models, and practical approaches to profitability analysis and valuation. In particular, none of the linear information models published to date exhibit an obvious role for profitability analysis. For example, in the standard Ohlson model, earnings and book value apparently summarise all the value relevant information available from the firm's financial statements and there is no apparent need for any further investigation of the accounting numbers beyond these specific line items. The purpose of this paper is to attempt to investigate potential analytical links between formal valuation models and practical profitability analysis. Specifically, we attempt to show how key features of practical profitability analysis might be incorporated into formal valuation models. In this respect there are two particular aspects of valuation practice to which the formal models published to date have paid no attention. First, in practice we often see explicit reference made to the demand side (sales), and supply side (costs) of the business. Second, we often see attempts to benchmark the financial ratios of one firm against the corresponding ratios of firms in the same industry. The purpose of this paper is to attempt to explain why such practices make sense in the context of an attempt to model the principal determinants of firm value within a residual income valuation framework.     

Hedging structured credit products during the credit crisis: A horse race of 10 models

Pricing and hedging structured credit products poses major challenges to financial institutions. This paper puts several valuation approaches through a crucial test: How did these models perform in one of the worst periods of economic history, September 2008, when Lehman Brothers went under? Did they produce reasonable hedging strategies? We study several bottom-up and top-down credit portfolio models and compute the resulting delta hedging strategies using either index contracts or a portfolio of single-name CDS contracts as hedging instruments. We compute the profit-and-loss profiles and assess the performances of these hedging strategies. Among all 10 pricing models that we consider the Student-t copula model performs best. The dynamical generalized-Poisson loss model is the best top-down model, but this model class has in general problems to hedge equity tranches. Our major finding is however that single-name and index CDS contracts are not appropriate instruments to hedge CDO tranches.     

Impact of multiple curve dynamics in credit valuation adjustments under collateralization

We present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework presented in Pallavicini et al. [Funding valuation adjustment: FVA consistent with CVA, DVA, WWR, collateral, netting and re-hyphotecation, 2011], and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such as basis swaps. We stress that a proper wrong way risk analysis for such products requires a model with a stochastic basis and we show numerical results confirming this fact.     

Warrant valuation and exercise strategy

This paper demonstrates that warrant valuation and exercise strategy differ fundamentally from call option valuation. Simultaneous exercise of warrants is shown to be suboptimal and a monopolist owning all warrants can achieve a higher value. Unless warrants are perfectly divisible, no satisfactory equilibrium exists for the valuation and exercise of widely held warrants. The problems encountered appear to be quite general and stem from necessary assumptions about future corporate dividend policy and capital structure. Such assumptions are necessary for any model of corporate security valuation.