LO 8.1: Evaluate the lim itations o f financial m odeling with respect to the model

LO 8.1: Evaluate the lim itations o f financial m odeling with respect to the model itself, calibration o f the model, and the m odels output.
Financial models are important tools to help individuals and institutions better understand the complexity of the financial world. Financial models always deal with uncertainty and are, therefore, only approximations of a very complex pricing system that is influenced by numerous dynamic factors. There are many different types of markets trading a variety of assets and financial products such as equities, bonds, structured products, derivatives, real estate, and exchange-traded funds. Data from multiple sources is then gathered to calibrate financial models.
Due to the complexity of the global financial system, it is important to recognize the limitations of financial models. Limitations arise in financial models as a result of inaccurate inputs, erroneous assumptions regarding asset variable distributions, and mathematical inconsistencies. Almost all financial models require market valuations as inputs. Unfortunately, these values are often determined by investors who do not always behave rationally. Therefore, asset values are sometimes random and may exhibit unexpected changes.
Financial models also require assumptions regarding the underlying distribution of the asset returns. Value at risk (VaR) models are used to estimate market risk, and these models often assume that asset returns follow a normal distribution. However, empirical studies actually find higher kurtosis in return distributions, which suggest a distribution with fatter tails than the normal distribution.
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2018 Kaplan, Inc.
Topic 8 Cross Reference to GARP Assigned Reading – Meissner, Chapter 3
.Another example of a shortcoming of financial models is illustrated with the Black-Scholes- Merton (BSM) option pricing model. The BSM option pricing model assumes strike prices have constant volatility. However, numerous empirical studies find higher volatility for out- of-the money options and a volatility skew in equity markets. Thus, option traders and risk managers often use a volatility smile (discussed in Topic 13) with higher volatilities for out- of-the money call and put options.
Financial models at times may fail to accurately measure risk due to mathematical inconsistencies. For example, regarding barrier options, when applying the BSM option pricing model to up-and-out calls and puts and down-and-out calls and puts, there are rare cases where the inputs make the model insensitive to changes in implied volatility and option maturity. This can occur when the knock-out strike price is equal to the strike price, and the interest rate equals the underlying asset return. Risk managers and traders need to be aware of the possibility of mathematical inconsistencies causing model risk that leads to incorrect pricing and the inability to properly hedge risk.
Lim itations in the Calibration o f Financial M odels
Financial models calibrate parameter inputs to reflect current market values. These parameters are then used in financial models to estimate market values with limited or no pricing information. The choice of time period used to calibrate the parameter inputs for the model can have a big impact on the results. For example, during the 2007 to 2009 financial crisis, risk managers used volatility and correlation estimates from pre-crisis periods. This resulted in significantly underestimating the risk for value at risk (VaR), credit value at risk (CVaR), and collateralized debt obligation (CDO) models.
All financial models should be tested using scenarios of extreme economic conditions. This process is referred to as stress testing. For example, VaR estimates are calculated in the event of a systemic financial crisis or severe recession. In 2012, the Federal Reserve, under the guidelines of Basel III, required all financial institutions to use stress tests.
Lim itations o f Financial M odel O utputs
Limitations of financial models became evident during the recent global financial crisis. Traders and risk managers used new copula correlation models to estimate values in collateralized debt obligation (CDO) models. The values of these structured products were linked to mortgages in a collapsing real estate market.
The copula correlation models failed for two reasons. First, the copula correlation models assumed a negative correlation between the equity and senior tranches of CDOs. However, during the crisis, the correlations for both tranches significantly increased causing losses for both. Second, the copula correlation models were calibrated using volatility and correlation estimates with data from time periods that had low risk, and correlations changed significantly during the crisis.
A major lesson learned from the global financial crisis is that copula models cannot be blindly trusted. There should always be an element of human judgment in assessing the risk associated with any financial model. This is especially true for extreme market conditions.
2018 Kaplan, Inc.
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Topic 8 Cross Reference to GARP Assigned Reading – Meissner, Chapter 3
S t a t i s t i c a l C o r r e l a t i o n M e a s u r e s

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