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Recently, domestic market participants have a growing interest in synthetic Collateralized Debt Obligation (CDO) as a security to reduce credit risk and create new profit. Therefore, the valuation method and hedging strategy for synthetic CDO become an important issue. However, there is no won-denominated credit default swap transactions, which are essential for activating synthetic CDO transaction‘ In addition, there is no transparent market information for the default probability, asset correlation, and recovery rate, which are critical variables determining the price of synthetic CDO.

This study first investigates the method of estimating the default probability, asset correlation coefficient, and recovery rate. Next, using five synthetiC CDO pricing models‘ widely used OFGC (One-Factor Non-Gaussian Copula) model. OFNGC (One-Factor Non-Gaussian Copula) model such as OFDTC (One-Factor Double T-distribution Copula) model of Hull and White (2004) or NIGC (Normal Inverse Gaussian Copula) model of Kalemanova et al.(2005), SC<Stochastic Correlation) model of Burtschell et al.(2005), and FL (Forward Loss) model of Bennani (2005), I Investigate and compare three points: 1) appropriateness for portfolio loss distribution, 2) explanation for standardized tranche spread, 3) sensitivity for delta-neutral hedging strategy. To compare pricing models, parameter estimation for each model is preceded by using the term structure of iTraxx Europe index spread and the tranch spreads with different maturities and exercise prices Remarkable results of this study are as follows. First, the probability for loss interval determining mezzanine tranche spread is lower in all models except SC model than OFGC model. This result shows that all mαdels except SC model in some degree solve the implied correlation smile phenomenon, where the correlation coefficient of mezzanine tranche must be lower than other tranches when OFGC model is used. Second, in explaining standardized tranche spread, NIGC model is the best among various models with respect to relative error. When OFGC model is compared with OFDTC model, OFOTC model is better than OFGC model in explaining 5-year tranche spreads. But for 7-year or 10-year tranches, OFDTC model is better with respect to absolute error while OFGC model is better with respect to relative error. Third, the sensitivity sign of senior tranctle spread with respect to asset correlation is sometime negative in NIG model while it is positive in other models. This result implies that a long position may be taken by the issuers of synthet.ic COO as a correlation delta-neutral hedging strategy when OFGC model is used, while a short position may be taken when NIGC model is used.

Both consumer and corporate credit ratings agencies played a major role in the US subprime mortgage crisis. Equifax, Experian, and TransUnion deployed a formalized scoring system to assess individuals in mortgage origination, mortgage pools then were assessed for securitization by Moody's, S&P, and Fitch relying on expert judgment aided by formal models. What can we learn about the limits of formalization from the crisis? We discuss five problems responsible for the rating failures – reactivity, endogeneity, learning, correlated outcomes, and conflict of interest – and compare the way consumer and corporate rating agencies tackled these difficulties. We conclude with some policy lessons.

How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black–Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-to-expiration, or times. The latter amounts to examining predictions of future implied volatilities.

Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better-performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option-pricing models might then be limited.

The implied volatility surface is the collection of volatilities implied by option contracts for different strike prices and time-to-maturity. We study factor models to capture the dynamics of this three-dimensional implied volatility surface. Three model types are considered to examine desirable features for representing the surface and its dynamics: a general dynamic factor model, restricted factor models designed to capture the key features of the surface along the moneyness and maturity dimensions, and in-between spline-based methods. Key findings are that: (i) the restricted and spline-based models are both rejected against the general dynamic factor model, (ii) the factors driving the surface are highly persistent, and (iii) for the restricted models option Δ is preferred over the more often used strike relative to spot price as measure for moneyness.

The purpose of this paper is to ascertain the pattern of the implied volatility function for currency options traded on the National Stock Exchange of India (NSE), identify its potential determinants and to investigate any seasonality in the pattern.

The paper examines four different specifications for the implied volatility smile of exchange-traded dollar-rupee options. These specifications are tested by running Ordinary Least Squares (OLS) regressions on a daily basis for all options over the entire sample period. Seven potential determinants for the shape of the volatility function are identified. Contemporaneous and lead-lag relationships between these determinants and the shape of the volatility function are examined using OLS and multivariate VAR. Impulse response functions are employed to test the strength and persistence of the lead-lag relations. Seasonality of the smile pattern is tested using OLS.

The study shows that the implied volatility function for dollar-rupee options is asymmetric and varies with the time to maturity of the option. Historical volatility, momentum and jumps in the exchange rate, time to maturity, traded volume of options and volatility in the stock market appear to Granger-cause the shape of the volatility smile. Feedback causality is observed from the shape of the smile to the volatility, momentum and jumps in the exchange rate and trading volume of currency options. A weak day-of-the-week effect is observed in the pattern of the volatility smile.

The study sheds light on the potential determinants of the smile and highlights the predictive power of the smile which findings can be useful to market practitioners for pricing and hedging of dollar-rupee options. The study has strong practical implications during a period of increased volatility in the dollar-rupee pair.

Most of the existing literature regarding implied volatility smiles has focused either on the volatility smile of US equity index options or that of major liquid currencies. There is a need for such studies in the context of options on emerging market currencies such as the Indian rupee which are characterized by thin trading and frequent central bank intervention and signaling. To the best of the author’s knowledge this study is the first to focus on the volatility smile of exchange-traded options on the US dollar–Indian rupee.

The aim of this study is to examine the “volatility smile” or/and “skew”, term structure and implied volatility surfaces based on those European options written in the standard and poor (S&P) Nifty equity index. The stochastic nature of implied volatility across strike price, time-to-expiration and moneyness violates the core assumption of the Black–Scholes option pricing model.

The potential determinants of implied volatility are the degree of moneyness, time-to-expiration and the liquidity of the strikes. The empirical work has been expressed by means of a simple ordinary least squares (OLS) framework and presents the estimation results according to moneyness, time-to-expiration and liquidity of options.

The options data give evidence of the existence of a classical U-shaped volatility smile for the Indian options market. Indeed, there is some evidence that the “volatility smirk” which pertains to 30-day options and also implied volatility remain higher for the shorter maturity options and decrease as the time-to-expiration increases. The results lead us to believe that in-the-money calls and out-of-the-money puts are of higher volatility than at-the-money options. Conclusion was drawn due to the persistence of the smile in the options market.

The practical implication of studying stylized patterns of implied volatility is that it educates the volatility traders about how in-the-money and out-of-the-money options are priced in the options market, and provides an estimate of volatility for the pricing of future options.

This study is an extension of previous work. The undertaking has been to examine the case of a more liquid and transparent options market, which is missing from the earlier work. The current study is more relevant because, since 2008, significant changes have been observed in the futures and options market in India.

This paper studies the pricing of collateralized debt obligation (CDO) using Monte Carlo and analytic methods. Both methods are developed within the framework of the reduced form model. One-factor Gaussian Copula is used for treating default correlations amongst the collateral portfolio. Based on the two methods, the portfolio loss, the expected loss in each CDO tranche, tranche spread, and the default delta sensitivity are analyzed with respect to different parameters such as maturity, default correlation, default intensity or hazard rate, and recovery rate. We provide a careful study of the effects of different parametric impact. Our results show that Monte Carlo method is slow and not robust in the calculation of default delta sensitivity. The analytic approach has comparative advantages for pricing CDO. We also employ empirical data to investigate the implied default correlation and base correlation of the CDO. The implication of extending the analytical approach to incorporating Levy processes is also discussed.

This paper analyzes implied volatilities (IVs), which are computed from trading records of the KOSPI 200 index option market from January 2005 to December 2014, to examine major characteristics of the market pricing behavior. The data includes only daily closing prices of option transactions for which the daily trading volume is larger than 300 contracts. The IV is computed using the Black-Scholes option pricing model. The empirical findings are as follows;

Firstly, daily averages of IVs have shown very similar behavior to historical volatilities computed from 60-day returns of the KOSPI 200 index. The correlation coefficient of IV of the ATM call options to historical volatility is 0.8679 and that of the ATM put options is 0.8479.

Secondly, when moneyness, which is measured by the ratio of the strike price to the spot price, is very large or very small, IVs of call and put options decrease days to maturity gets longer. This is partial evidence of the jump risk inherent in the stochastic process of the spot price.

Thirdly, the moneyness pattern showed heavily skewed shapes of volatility smiles, which was more apparent during the global financial crises period from 2007 to 2009. Behavioral reasons can explain the volatility smiles. When the moneyness is very small, the deep OTM puts are priced relatively higher due to investors’ crash phobia and the deep ITM calls are valued higher due to investors’ overconfidence and confirmation biases. When the moneyness is very large, the deep OTM calls are priced higher due to investors’ hike expectation and the deep ITM puts are valued higher due to overconfidence and confirmation biases.

Fourthly, for almost all moneyness classes and for all sub-periods, the IVs of puts are larger than the IVs of calls. Also, the differences of IVs of deep OTM put ranges minus IVs of deep OTM calls, which is known to be a measure of crash phobia or hike expectation, shows consistent positive values for all sub-periods. The difference in the financial crisis period is much bigger than in other periods. This suggests that option traders had a stronger crash phobia in the financial crisis.

This chapter analyzes the empirical performance of alternative option pricing models using Black and Scholes (1973) as a benchmark. Specifically, we consider the Heston (1993) and Corrado and Su (1996) models and price call options on the S&P 500 index over the period from November 2010 to April 2011, evaluating each model by computing in- and out-of-sample pricing errors. We find that the two proposed models reduce both types of errors and mitigate the smile effect with respect to the benchmark. Moreover, in most of the cases, the model in Corrado and Su (1996) beats that in Heston (1993). Then, we conclude that skewness and kurtosis matter for option pricing purposes.

The purpose of this paper is to assign fair values to options reduces to the attempt to attribute correct implied volatilities. Here, the authors extend the study by Tanha et al. (2014) to determine the impact of macro economic announcements on the option smile.

First, the authors estimate the implied volatility function in terms of moneyness. The authors next analyse the impact of macroeconomic announcements on the estimated coefficients (b ₀, b ₁, b ₂) by regressing the coefficients on the macroeconomic announcements.

The authors find that in-the-money options are sensitive to such announcements, but that out-of-the money options are not. This is consistent with the interpretation of investor behaviour from prospect theory.

The systematic pricing errors that have been documented using the Black-Scholes model have stimulated attempts to improve the model predictions. The approach uses DVF model to improve the B-S model.