Juliusz Jablecki

A model for dependent defaults and pricing contingent claims with counterparty risk

This paper presents a new, intuitive but mathematically powerful model of dependent defaults and derives a general framework for pricing products whose values depend on credit correlation between the counterparty and the reference entity. The dependence framework is a natural extension of the Gaussian factor approach, which can be applied in the context of reduced form credit risk models, allowing i.a. for stochastic hazard and recovery rates. The prices of plain vanilla credit default swaps, first-to-default swaps and default swaptions are derived as particular examples.

Modeling Joint Defaults in Correlation-Sensitive Instruments

This paper presents a simple model for joint defaults and shows how it can be applied to pricing and risk-managing instruments that are sensitive to credit correlation, from simple repos to collateralized debt obligations. The model relies on a conservative and intuitive representation of a systematic factor as a chain of dependencies running through the whole economy. This allows capturing the concentration of defaults in time and endogenously produces dynamics of default correlation as the model output rather than its input.

Volatility as a New Class of Assets? The Advantages of Using Volatility Index Futures in Investment Strategies

This paper investigates the changes in the investment portfolio performance after including VIX. We apply different models for optimal portfolio selection (Markowitz and Black-Litterman) assuming both the possibility of short sale and the lack of it. We also use various assets, data frequencies, and investment horizons to get a comprehensive picture of our results’ robustness. Investment strategies including VIX futures do not always deliver higher returns or higher Sharpe ratios for the period 2006-2013. Their performance is quite sensitive to changes in model parameters. However, including VIX significantly increases the returns in almost all cases during the recent financial crisis. This result clearly emphasizes potential gains of having such an asset in the portfolio in case of very high volatility in financial markets.

Does Historical Volatility Term Structure Contain Valuable Information for Predicting Volatility and Index Futures

We suggest that the term structure of volatility futures (e.g. VIX futures) shows a clear pattern of dependence on the current level of VIX index. At the low level of VIX (below 20) the term structure is highly upward sloping; at the high VIX level (over 30) it is strongly downward sloping. We use those features to better predict future volatility and index futures. We begin by introducing some quantitative measures of volatility term structure (VTS) and volatility risk premium (VRP). We use them further to estimate the distance between the actual value and the fair (model) value of the VTS. We find that this distance has significant predictive power for volatility futures and index futures and we use this feature to design a simple strategy to invest in VIX index futures and S&P500.

Options Delta Hedging with No Options at All

The adjustment speed of delta hedged options exposure depends on the market realized and implied volatility. We observe that by consistently hedging long and short positions in options we can eventually end up with pure exposure to volatility without any options in the portfolio at all. The results of such arbitrage strategy is based only on speed of adjustment of delta hedged option positions. More specifically, they rely on interrelation between realized volatility levels calculated for various time intervals (from daily to intraday frequency). Theoretical intuition enables us to solve the puzzle of the optimal frequency of hedge adjustment and its influence on hedging efficiency. We present results of a simple hedge strategy based on the consistent hedging of a portfolio of options for various worldwide equity indice

Estimating the Risk of Joint Defaults: An Application to Central Bank Collateralized Lending Operations

Central bank lending to commercial banks is typically collateralized which reduces central bank’s credit risk exposure to “double default events” when the counterparty and the issuer of the underlying collateral asset both default in a short period of time. This paper presents a simple model for correlated defaults which are the key drivers of residual credit risk in central bank’s repo portfolios. In the model default times of counterparties and collateral issuers are determined by idiosyncratic and systematic factors, whereby a name defaults if it is struck by either factor for the first time. The novelty of our approach lies in representing systematic factors as increasing sequences of random variables. Such a setting allows to build a rich dependence structure that is free of the flaws inherent in the Gaussian copula-based approaches currently regarded as state of the art solutions for central banks.