Integrated modelling of credit and equity market risk
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NO FULL TEXT AVAILABLE. Access is restricted indefinitely. ----- The rapid growth in popularity of credit default swaps (CDS) in recent years has meant liquid markets now exist for trading both equity and credit derivatives on the same firm. This has seen the introduction of hybrids derivatives, such as equity default swaps (EDS), which have both credit- and equity-like features. The current global financial crisis has highlighted the interdependence that exists between the credit and equity markets and signalled the importance of a unified approach to pricing hybrids that is consistent with prices of actively traded CDS and options. Under a framework whereby the stock price follows a diffusion process with a jump to default (zero), expressions for European option prices and the risk neutral probability of default can be derived. Such models can then be jointly calibrated to the term structure of CDS spreads and the implied volatility of equity options, and subsequently used to price more exotic, illiquid or over-the-counter derivatives. While the main contribution of this thesis is theoretical in nature, it is motivated by an initial empirical study focusing on five US firms spanning periods both before and after the current financial crisis. To capture the uncertainty in the options market, and minimise the synchronisation error with stock prices, intra-day quote data is used. Rather than make explicit assumptions regarding future dividends, we determine an implied dividend from option prices, and fit volatility smiles for each maturity using a local linear smoother. To better understand the links between credit and equity markets, we use firm-specific variables suggested by structural models to investigate the contemporaneous and inter-temporal determinants of CDS spreads. Such knowledge is important not only for risk managers and traders, but for ensuring that pricing models are consistent with empirical observations. We evaluate a number of different models that fall within this framework. We take the constant elasticity of variance (CEV) model as a starting point as it captures the observed relationships that exist between equity returns, volatility, and CDS spreads. The model is then extended to incorporate a jump to default to provide a better fit to short term CDS spreads. We find that a model with time homogeneous parameters is unable to simultaneously match the entire volatility surface and CDS spread curve, that the fit increases with the credit quality of the firm, and that the ratio of EDS to CDS spreads is consistent with those observed in the market.
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