Pricing CDOs with state-dependent stochastic recovery rates

Up to the 2007 crisis, research within bottom-up CDO models mainly concentrated on the dependence between defaults. Since then, due to substantial increases in market prices of systemic credit risk protection, more attention has been paid to recovery rate assumptions. In this paper, we use stochastic orders theory to assess the impact of recovery on CDOs and show that, in a factor copula framework, a decrease of recovery rates leads to an increase of the expected loss on senior tranches, even though the expected loss on the portfolio is kept fixed. This result applies to a wide range of latent factor models and is not specific to the Gaussian copula model. We then suggest introducing stochastic recovery rates in such a way that the conditional on the factor expected loss (or, equivalently, the large portfolio approximation) is the same as in the recovery markdown case. However, granular portfolios behave differently. We show that a markdown is associated with riskier portfolios than when using the stochastic recovery rate framework. As a consequence, the expected loss on a senior tranche is larger in the former case, whatever the attachment point. We also deal with implementation and numerical issues related to the pricing of CDOs within the stochastic recovery rate framework. Due to differences across names regarding the conditional (on the factor) losses given default, the standard recursion approach becomes problematic. We suggest approximating the conditional on the factor loss distributions, through expansions around some base distribution. Finally, we show that the independence and comonotonic cases provide some easy to compute bounds on expected losses of senior or equity tranches.     

Delta-hedging correlation risk?

While the Gaussian copula model is commonly used as a static quotation device for CDO tranches, its use for hedging is questionable. In particular, the spread delta computed from the Gaussian copula model assumes constant base correlations, whereas we show that the correlations are dynamic and correlated to the index spread. It might therefore be expected that a dynamic model of credit risk, which is able to capture the dependence between the base correlations and the index spread, will have better hedging performances. In this paper, we compare delta hedging of spread risk based on the Gaussian copula model, to the implementation of jump-to-default ratio computed from the dynamic local intensity model. Theoretical and empirical analysis are illustrated by using the market data in both before and after the subprime crisis. We observe that delta hedging of spread risk outperforms the implementation of jump-to-default ratio in the pre-crisis period associated with CDX.NA.IG series 5, and the two strategies have comparable performance for crisis period associated with CDX.NA.IG series 9 and 10. This shows that, although the local intensity model is a dynamic model, it is not sufficient to explain the joint dynamic of the index spread and the base correlations, and a richer dynamic model is required to obtain better hedging results. Moreover, although different specifications of the local intensity can be fitted to the market data equally well, their hedging results can be significant different. This reveals substantial model risk when hedging CDO tranches.     

Are All Ratings Created Equal? The Impact of Issuer Size on the Pricing of Mortgage‐Backed Securities

Initial yields on both AAA‐rated and non‐AAA rated mortgage‐backed security (MBS) tranches sold by large issuers are higher than yields on similar tranches sold by small issuers during the market boom years of 2004 to 2006. Moreover, the prices of MBS sold by large issuers drop more than those sold by small issuers, and the differences are concentrated among tranches issued during 2004 to 2006. These results suggest that investors price the risk that large issuers received more inflated ratings than small issuers, especially during boom periods.     

Valuation of collateralized debt obligations with hierarchical Archimedean copulae

Modelling portfolio credit risk is one of the crucial challenges faced by financial services industry in the last few years. We propose the valuation model of collateralized debt obligations (CDO) based on hierarchical Archimedean copulae (HAC) with up to three parameters, with default intensities calibrated to market data and with random loss given defaults that are correlated with default times. The methods presented are used to reproduce the spreads of the iTraxx Europe tranches. Our approach describes the market prices better than the standard pricing procedure based on the Gaussian distribution. We also obtain a flat correlation smile across tranches thereby solving the implied correlation puzzle.     

An Empirical Analysis of the Pricing of Collateralized Debt Obligations

We use the information in collateralized debt obligations (CDO) prices to study market expectations about how corporate defaults cluster. A three‐factor portfolio credit model explains virtually all of the time‐series and cross‐sectional variation in an extensive data set of CDX index tranche prices. Tranches are priced as if losses of 0.4%, 6%, and 35% of the portfolio occur with expected frequencies of 1.2, 41.5, and 763 years, respectively. On average, 65% of the CDX spread is due to firm‐specific default risk, 27% to clustered industry or sector default risk, and 8% to catastrophic or systemic default risk.     

限制交易政策如何影响期现关系?——对股指期货价格发现功能的实证检验

本文利用2015年中国股市大幅下跌期间,对股指期货严格限制交易政策这一独特事件前后的高频数据,研究限制交易政策对股指期货与股票市场价格引导关系的影响。利用I-S模型和分位数回归方法的实证结果表明:限制交易政策实施前,股指期货对股票市场的价格影响更强,尤其表现在价格急剧下跌时期;限制交易政策显著增加了期货市场交易成本,从而降低了期货市场的信息份额,削弱了其对股票市场的价格影响,并且改变了期货价格对现货价格“助跌强于助涨”的影响模式,增强了股指期货在价格上涨时对股票市场的影响。研究结果一方面直接量化了期货交易成本变动对其价格发现功能的负面影响,另一方面也从价格引导关系的视角提供了股市危机时期股指期货限制交易政策监管效果的实证证据。     

Copula dynamics in CDOs

Values of tranche spreads of collateralized debt obligations (CDOs) are driven by the joint default performance of the assets in the collateral pool. The dependence between the entities in the portfolio mainly depends on current economic conditions. Therefore, a correlation implied from tranches can be seen as a measure of the general situation of the credit market. We analyse the European market of standardized CDOs using tranches of the iTraxx index in the periods before and during the global financial crisis. We investigate the evolution of the correlations using different copula models: the standard Gaussian, the NIG, the double-t, and the Gumbel copula model. After calibration of these models, one obtains a time varying vector of parameters. We analyse the dynamic pattern of these coefficients. That enables us to forecast future parameters and consequently calculate Value-at-Risk measures for iTraxx Europe tranches.     

Securitization bubbles: Structured finance with disagreement about default risk

An additional reason for the structured finance boom of the 2000s may have been disagreement about default risk of collateral assets. When risk-neutral investors disagree about average default probabilities, structuring collateral cash flow raises prices by concentrating optimists’ demand on risky tranches. With disagreement about default correlation, low-correlation investors believe in diversification and pay high prices for senior tranches they deem riskless. High-correlation investors value junior tranches they expect to pay whenever aggregate conditions are good. Risk aversion and short selling through credit default swaps reduce the prices of both pass-through and structured securitizations but may increase the return to tranching.     

Rollover Risk and Market Freezes

The debt capacity of an asset is the maximum amount that can be borrowed using the asset as collateral. We model a sudden collapse in the debt capacity of good collateral. We assume short‐term debt that must be frequently rolled over, a small transaction cost of selling collateral in the event of default, and a small probability of meeting a buy‐to‐hold investor. We then show that a small change in the asset's fundamental value can be associated with a catastrophic drop in the debt capacity, the kind of market freeze observed during the crisis of 2007 to 2008.     

Looking Beyond Credit Ratings: Factors Investors Consider In Pricing European Asset‐Backed Securities

In this paper, we empirically investigate what credit factors investors rely upon when pricing the spread at issue for European asset‐backed securities. More specifically, we investigate how credit factors affect new issuance spreads after taking into account credit rating. We do so by investigating primary market spreads for tranches of non‐mortgage‐related asset‐backed securities issued from 1999 to the year prior to the subprime mortgage crisis, 2007. We find that although credit ratings play a major role in determining spreads, investors appear to not rely exclusively on these ratings. Our findings strongly suggest that investors do not ignore other credit factors beyond the assigned credit rating.     

An analytical approach for systematic risk sensitivity of structured finance products

The global financial crisis has shown that many financial institutions dealing with credit derivatives were exposed to severe unexpected losses. This indicates that systematic influences are decisively underestimated particularly with regard to structured products like securitized tranches of collateralized debt obligations. Our analytical study addresses these systematic effects: We provide a simple model which allows a closed-form comparison of both bonds and tranches with respect to their systematic risk. We demonstrate that the exposure to systematic risk of tranches may be many times higher than the exposure of bonds, even if both products share the same rating grade, e.g., an ‘AAA’ rating, measured by either default probability or expected loss. Particularly in economic downturns, default rates of tranches may be multiples of those of bonds. Our results help understand high default rates of tranches during the financial crisis and show that classical ratings are insufficient metrics for measuring risks of structured products.     

Yes We Can (Price Derivatives on Survivor Indices)

We propose a simulation approach to value derivatives when the underlying dynamics are estimated using the survivor indices directly. Our results show that survivor forward and swap premiums increase with maturity and with the market price of risk. Our results also confirm that taking the optionality into consideration is important from a pricing perspective, for both U.S. women and men. We compare our results to what is obtained using an alternative modeling approach in which a Lee–Carter model is used to indirectly model the survivor index. Compared to this method, our estimated premiums and prices are higher for all longevity products. Moreover, comparing American‐style with European‐style options we find that, although the early exercise option has value when using survivor indices directly, the relative value of the early exercise option is significantly less than when the Lee–Carter model is used to indirectly model the survivor index. It follows that the assumed mortality dynamics have important implications for the term structure of forward and swap premiums and for the effect that changes in the market price of risk has on them.     

CDOs and the financial crisis: Credit ratings and fair premia

We study risk and return characteristics of CDOs using the market standard models. We find that fair spreads on CDO tranches are much higher than fair spreads on similarly-rated corporate bonds. Our results imply that credit ratings are not sufficient for pricing, which is surprising given their central role in structured finance markets. This illustrates limitations of the rating methodologies that are solely based on real-world default probabilities or expected losses and do not capture risk premia. We also demonstrate that CDO tranches have large exposure to systematic risk and thus their ratings and prices are likely to decline substantially when credit conditions deteriorate.     

Market segmentation and price differentials between A shares and H shares in the Chinese stock markets

We find that the risk premiums associated with the Hong Kong and mainland Chinese markets in a two-factor model successfully explain the cross section of returns on the A and H shares. Discounts of H-share prices relative to A-share prices are related to the contemporaneous movements of the H-share local market index relative to the A-share local market index, especially during the period of the Asian financial crisis, as well as the spread of savings rates between Hong Kong and mainland China. The evidence suggests that the risk premiums associated with the segmented A-share and H-share markets exert crucial impacts on the price differentials between the two classes of shares.     

Marking‐to‐Market: Panacea or Pandora's Box?

Financial institutions have been at the forefront of the debate on the controversial shift in international standards from historical cost accounting to mark‐to‐market accounting. We show that the trade‐offs at stake in this debate are far from one‐sided. While the historical cost regime leads to some inefficiencies, marking‐to‐market may lead to other types of inefficiencies by injecting artificial risk that degrades the information value of prices, and induces suboptimal real decisions. We construct a framework that can weigh the pros and cons. We find that the damage done by marking‐to‐market is greatest when claims are (1) long–lived, (2) illiquid, and (3) senior. These are precisely the attributes of the key balance sheet items of banks and insurance companies. Our results therefore shed light on why banks and insurance companies have been the most vocal opponents of the shift to marking‐to‐market.     

TESTING THE NET BUYING PRESSURE HYPOTHESIS DURING THE ASIAN FINANCIAL CRISIS: EVIDENCE FROM HANG SENG INDEX OPTIONS

We investigate net buying pressure in the Hong Kong Hang Seng Index options market during the Asian financial crisis from July 1997 to August 1998. Our findings suggest that during this period, the dramatic changes in volatility overwhelmed the dynamics of supply and demand in the options market. The extremely high realized volatility drove market participants' expectations about future market volatility in the early months of the crisis. Findings during the late‐crisis, pre‐crisis, and post‐crisis periods are consistent with the net buying pressure hypothesis.     

Joint Dynamics of House Prices and Foreclosures

This paper studies the joint transitional dynamics of the foreclosures and house prices in a standard life‐cycle incomplete markets model with housing and a realistic long‐term mortgage structure. We calibrate our model to match several long‐term features of the U.S. housing market, and analyze the effects of several unexpected and permanent shocks on the house price and the foreclosure rate both across the steady states and along the transition between the steady states. We examine permanent, unexpected shocks to the risk‐free interest rate, the minimum down‐payment ratio, and unemployment. During the transition, these shocks create large movements in house prices. More importantly, the foreclosure dynamics are quite significant along the transition compared to the steady‐state changes, and there are strong feedbacks between foreclosures and house prices. We assess the effects of a temporary reduction in the risk‐free interest rate, which has moderate effects on house prices but little effect on foreclosure dynamics. We also study the effects of an ex ante macroprudential policy, which establishes a minimum down‐payment requirement at a higher threshold. Such a macroprudential policy helps substantially stabilize both house prices and foreclosures.     

Asymmetric dynamic relations between stock prices and mutual fund units in Japan. An application of hidden cointegration technique

This paper examines “causality” effects between mutual fund flows and stock index prices in Japan. In particular, both the short and long run dynamics between stock prices and fund units are investigated. The novelty of our paper is the use of the hidden cointegration technique which attempts to capture heterogeneous fund flow reactions when stock index prices move up or down. Moreover, we employ the crouching error correction model (CECM) to assess the relationship between stock market movements and fund flow changes. The results show that stock prices and mutual fund units are cointegrated. In the case of positive movements there is a bi-directional effect interconnecting them, whereas for negative movements, causality runs only from fund flows to stock prices. The dynamics structure provides evidence that market microstructure, taxation and investors' sentiment affect stock price and unit formation.     

Diversification Benefits of iShares and Closed-End Country Funds

We study the performance and diversification of iShares and their rival closed‐end country funds from April 1996 to December 1999. International iShares are country‐specific series of securities that track the price and yield of a specific Morgan Stanley Capital Internation (MSCI) country index and, presumably, should provide diversification benefits. Our single‐index model demonstrates that iShares replicate the home index, showing some potential for diversification. However, our two‐factor model, which isolates the “true” diversification virtues, documents that both iShares and closed‐end country fund market prices maintain considerable exposure to the U.S. market. Furthermore, the net asset value returns of the closed‐end funds demonstrate a strong home country exposure, suggesting there is no substitute for direct foreign investment.     

Securitization of Longevity Risk Using Percentile Tranching

Securitizations that transfer risk to the financial markets are a potential solution to longevity risk in the annuity business. The classical Lee–Carter model is applied to generate the future stochastic survival distribution. A method to design inverse survivor bonds using percentile tranches and to calculate the security prices is presented. The percentile tranche method is a simple and practical way for the issuer to design and price the security. This method can serve to identify the risk–yield relationship, which can provide investors with clear insight regarding the appropriate choice of tranches.