International Journal of Theoretical and Applied Finance

Numerous incidents in the financial world have exposed the need for the design and analysis of models for correlated default timings. Some models have been studied in this regard which can capture the feedback in case of a major credit event. We extend the research in the same direction by proposing a new family of models having the feedback phenomena and capturing the effects of regime switching economy on the market. The regime switching economy is modeled by a continuous time Markov chain. The Markov chain may also be interpreted to represent the credit rating of the firm whose bond we seek to price. We model the default intensity in a pool of firms using the Markov chain and a risk factor process. We price some single-name and multi-name credit derivatives in terms of certain transforms of the default and loss processes. These transforms can be calculated explicitly in case the default intensity is modeled as a linear function of a conditionally affine jump diffusion process. In such a case, under suitable technical conditions, the price of credit derivatives are obtained as solutions to a system of ODEs with weak coupling, subject to appropriate terminal conditions. Solving the system of ODEs numerically, we analyze the credit derivative spreads and compare their behavior with the nonswitching counterparts. We show that our model can easily incorporate the effects of business cycle. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low floating interest rate, high default intensity rate, and high volatility. We also model the effects of firm restructuring on the credit spread, in case of a default.

This paper proposes a model for pricing credit derivatives in a defaultable HJM framework. The model features hump-shaped, level dependent, and unspanned stochastic volatility, and accommodates a correlation structure between the stochastic volatility, the default-free interest rates, and the credit spreads. The model is finite-dimensional, and leads (a) to exponentially affine default-free and defaultable bond prices, and (b) to an approximation for pricing credit default swaps and swaptions in terms of defaultable bond prices with varying maturities. A numerical study demonstrates that the model captures stylized various features of credit default swaps and swaptions.

In this paper, we analyze factor uniqueness in the S&P 500 universe. The current theory of approximate factor models applies to infinite markets. In the limit of infinite markets, factors are unique and can be represented with principal components. If this theory would apply to realistic markets such as the S&P 500 universe, the quest for proprietary factors would be futile. We find that this is not the case: in finite markets of the size of the S&P 500 universe different factor models can indeed coexist. We compare three dynamic factor models: a factor model based on principal component analysis, a classical factor model based on industry, and a factor model based on cluster analysis. Dynamic behavior is represented by fitting vector autoregressive models to factors and using them to make forecasts. We analyze the uniqueness of factors using Procrustes analysis and correlation analysis. Forecasting performance of the factor models is analyzed by forming active portfolio strategies based on the forecasts for each model using sample data from the S&P 500 index in the 21-year period 1989–2010. We find that one or two factors which we can identify with global factors are common to all models, while the other factors for the factor models we analyzed are truly different. Models exhibit significant differences in performance with principal component analysis-based factor models appearing to behave better than the sector-based factor models.

This paper investigates a structural credit default model that is based on a hyper-exponential jump diffusion process for the value of the firm. For credit default swap prices and other quantities of interest, explicit expressions for the corresponding Laplace transforms are derived. The time-dynamics of the model are studied, particularly the jumps in credit spreads, the understanding of which is crucial e.g. for the pricing of gap risk. As an application of our findings, the model is calibrated to credit default swap spreads observed in the market.

In this paper, we study the intersection between the price of a European put and its payoff function. We derive asymptotic expansion formulas for the intersection near expiration date for three different cases of risk-free rate r and dividend yield q, i.e. r > q, r = q, and r < q. The comparison with those of the critical stock price of an American option enhances our understanding on the convergence of the asymptotic expansion near a singular point.

We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, at low and high volatilities, with different qualitative behavior. The two regimes are separated by a sharp transition, which is similar to a phase transition in condensed matter physics. We study the behavior of the model in the large volatility phase, and discuss the implications of the phase transition for the pricing of interest rates derivatives. In the large volatility phase, certain expectation values and convexity adjustments have an explosive behavior. For sufficiently low volatilities the caplet smile is log-normal to a very good approximation, while in the large volatility phase the model develops a non-trivial caplet skew. The phenomenon discussed here imposes thus an upper limit on the volatilities for which the model behaves as intended.

This paper consists of two parts. The first part aims to construct a LIBOR market model under the real-world measure (LMRW) according to the Jamshidian framework. Then, LIBOR rates, bond prices and a state price deflator are explicitly described under the LMRW. The second part aims to estimate the market price of risk, as well as to investigate the fundamental properties of real-world simulations. Then, the following subjects are theoretically investigated: (1) a method for determining the number of factors for real-world simulations, (2) the properties of real-world simulations, and (3) the value of the market price of risk in connection with sample data. Numerical examples demonstrate our results.