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Fair Value Measurement of Exotic Options: Volatility Assumptions and Model Misspecification Error

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Fair Value Measurement of Exotic Options: Volatility Assumptions and Model Misspecification Error 67a FAIR VALUE MEASUREMENT OF EXOTIC OPTIONS: VOLATILITY ASSUMPTIONS AND MODEL MISSPECIFICATION ERROR Jacinto Marabel-Romo BBVA and University of Alcalá, Spain Andrés Guiral* Yonsei University, South Korea José Luis Crespo-Espert University of Alcalá, Spain José A. Gonzalo University of Alcalá, Spain Doocheol Moon Yonsei University, South Korea Áreas temáticas A) (Contabilidad) o B (Valoración y Finanzas) Acknowledgments: This paper has benefited greatly from comments and suggestionsby Christopher Humhprey, German Lopez-Espinosa, ManuelIllueca, Emiliano Ruiz and workshop participants at the VIII Workshop on Empirical Research in Financial Accounting, Seville, 2011. The authors acknowledge the support of the Spanish Ministry of Economy and Economy and Competitiveness thought the Project ECO2010-17463. *Corresponding author FAIR VALUE MEASUREMENT OF EXOTIC OPTIONS: VOLATILITY ASSUMPTIONS AND MODEL MISSPECIFICATION ERROR Abstract Fair Value Accounting (FVA) provides more relevant information to financial statement users, but there are also some concerns about the use of FVA resulting from the reliability of their estimations. We argue thatFVA canlead bank managers towards model misspecification error in the valuation of complex financial instruments traded in illiquid markets. This situation is especially problematic considering the high exposure to the aforementioned error of large U.S. and European banks. Further, recent research in auditing suggests that auditors are not in the best position to evaluate complex estimates due to standard uncertainty and lack of training/skills in this area. By pricing two common exotic derivatives (cliquet and barrier options), we illustrate the existence of model misspecification error when comparingtwo different but commonly used assumptions of volatility (i.e., local volatility vs. stochastic volatility). Our findings have important implications for bothaccounting and auditingstandard setters and bank regulators. Keywords:Fair value, exotic options, model misspecification error, implied volatility, local volatility, stochastic volatility. JEL:G12, M42. 2 1. Introduction The subprime crisis has provoked intense debate about the accounting rules employed by banks, especiallyon the use of fair value accounting (FVA) for financial instrument (Cheng 2012; Laux and Leuz 2009; Chen et al. 2013).1Initially, the major controversyrelied on the possibility that FVA contributed to the Financial Crisis or, at least, exacerbated its severity (Kothari and Lester 2012). However, recent research indicates that FVA played little or even no role in the Financial Crisis (Laux and Leuz 2010; Barth and Landsman 2010). It seems now that users, standard setters and the academia understand better that FVA measurements and other estimates provide benefits interms of higher potential relevance to users than would be provided by previous accounting measures, such as historical cost (Ahmed et al. 2011; Barth and Taylor 2010;Barth et al. 2001; Christensen et al. 2012; Song et al. 2010). Rather than FVA,it seems that one of the reasons of the Financial Crisiscould bethe use of inadequate models to valuate complex financial instruments (Derman and Wilmott 2009). The question is not anymore if we should accept FVA or not (Barth 2006). The remaining issue is how to estimateFVA and, particularly, in the case of extreme fair value measurements. While FVA provides more relevant information to financial statement users, some concerns focus onthe reliability of fair value estimation (Barth 2004). Fair value measurements in the absence of observed price might be unreliable due to intrinsic measurement error (noise) and management- induced error (bias) (Song et al. 2012). Prior studies provide evidence that managers may manipulate inputs for fair value estimates for their own interests (e.g., Aboody et al. 2006; Bartov et al. 2007; Dechow et al. 2010; Choudhary 2011). However, few studies examine fair value measurement error. Our fundamental objective is to analyze whether fair value measurements are subject to model misspecification. According to the International Accounting Standard Board, fair value is “the price thatwould be received to sell an asset or paidto transfer a liability in an orderly transactionbetween market 1Typically, financial instruments represent more than 90 percent of the assets and liabilities of bank holding companies and large investments banks (Laux and Leuz 2010, Hirst et al. 2004). 3 participants at themeasurement date” (IFRS No. 13).2The standard also introduces the conceptof a fair value hierarchy based on theobservability of the inputs. This hierarchyprioritizes the inputs used to measure fair values into three broadlevels. Level 1inputs are quoted prices in active markets foridentical assets or liabilities (i.e., pure mark-to-market). Level 2valuations are based on directly or indirectly observablemarket data for similar or comparable assets or liabilities.Two types of valuations aretypically distinguished within Level 2: (i) adjusted mark-to-market relies on quoted market pricesin active markets for similar items, or in inactive markets for identical items; (ii) mark-to-modelvaluation uses such inputs as yield curves, exchange rates, implied volatilities, credit spreads empirical correlations, etc.Level 3 valuationsare based on unobservable inputs that reflect the reporting entity’s own assumptions (i.e., pure mark-to-model).3 The standard gives highest priority to (unadjusted) quoted prices in active markets for identical assetsor liabilities and the lowest priority to unobservable inputs. Level 1 inputs, i.e., those with market prices, are the only ones truly meeting the definition of fair value,makingthe information asymmetry between preparers and users very low (Song et al. 2010). However, the standard is silent regarding any difficulties related to market friction, including those resulting from imperfect and incomplete markets (Meder et al. 2011). Thus, thecontroversial part of the standard is how to value an asset or a liability when an active market does not exist, i.e., in the case of Level 2 and Level 3valuations (Badertscher et al. 2012).Since it is difficult for users to observe directly how bank managers adapt those inputs to generate reported fairvalues, the information asymmetry between preparers and users is expected to be very high for Level 2 and Level 3 fair value estimates. Furthermore,in comparison to Level 1 fair values estimates, Level 2 and Level 3 fair value estimates are more costly to determine (Benston 2008) and very difficult for auditors to verify (Bell and Griffin 2The Financial Accounting Standard Board, i.e. the U.S. accounting standard setter, defines fair value in a similar way (SFAS 157). 3 Examples of financial instruments classified as Level 1 fair value estimates include treasuries, derivatives, equity and cash products when all of them are traded on high-liquidity exchanges.Examples of Level 2 fair value estimates include many over-the-counter (OTC) derivatives, such as interest rate swaps, foreign currency swaps, commodity swaps, and certain options and forward contracts.Other financial instruments classified as Level 2 are mortgage-backed securities, mortgage loans, many investment-grade listed credit bonds, some credit default swaps (CDS), many collateralized debt obligations (CDO), and less-liquid equity instruments.Examples of Level 3 estimates include complex and highly structured derivatives, distressed debt, highly-structured bonds, illiquid asset-backed securities (ABS), illiquid CDOs, private equity placements, and illiquid loans. 4 2012; Bratten et al. 2013).4For these reasons, fair value estimatesof complex or illiquid financial instrumentshave been denoted by critics as “marking to myth” (Bratten et al. 2012; Meder et al. 2011). The problem with the fair value hierarchy is that fair value measurements in the absence of observed prices might be unreliable due tointrinsic model misspecification error(Barth 2004; Song et al. 2010; Derman and Wilmott 2009).Model misspecification erroris rooted in the nonexistence of well-developed models to estimate fair values of all assets and liabilities (Barth 2004).This errorcan be defined as the risk to use a valuation model that does not reflect the market conditions for a financial instrument at a particular point of the time. An inadequate valuationmodel produces wrong measures that disturb the decision making process, either internally or externally, and could denyall the benefits associated with the use of FVA if the amount of the associated estimate error is material.5While for Level 1 fair value estimates the exposure to model misspecification error is minimum, for Level 2 and 3 fair values model misspecification error depends on the precision of the estimates (Barth 2004). In recent years there has been a remarkable growth of structured products with embedded exotic options (Hull and Suo 2002). These exotic options are a clear example of Level 2 valuations (i.e., mark-to-model) which are quite model dependent. Financial institutions that commercialize these structured products are exposed to the existence of model misspecification risk. The key point of the model misspecification risk is that different models can yield the same price for plain vanillaoptions but, at the same time, very different prices for complex exotic options depending on their assumptions corresponding to the evolution of the underlying asset price and its volatility.6 In this article, we consider the model misspecification
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