Credit derivatives and risk aversion

Abstract

We discuss the valuation of credit derivatives in extreme regimes such as when the time-tomaturity is short, or when payoff is contingent upon a large number of defaults, as with senior tranches of collateralized debt obligations. In these cases, risk aversion may play an important role, especially when there is little liquidity, and utility indifference valuation may apply. Specifically, we analyze how short-term yield spreads from defaultable bonds in a structural model may be raised due to investor risk aversion.

Accounting for risk aversion in derivatives purchase timing

“…After default, the firm's stock is no longer tradable, so the investor liquidates holdings in the stock and deposits in the money market account (with zero interest rate). Following Leung et al (2008) and Sircar and Zariphopoulou (2010), we assume a full pre-default market value on stock holdings upon liquidation. Hence, on {ζ t ≤ T }, the wealth is X u = X ζt for u ∈ (ζ t , T ].…”

“…For this extended problem, tractable representations may be straightforwardly obtained using the above methods under exponential utility. We can also treat many other parametric models, including stochastic volatility models (Sircar and Zariphopoulou, 2005) and credit risk models (Leung et al, 2008;Jaimungal and Sigloch, 2010) where closed-form expressions and dual representations are available for exponential indifference prices. It will certainly be interesting and challenging to consider derivative trading under other risk preferences.…”

“…To illustrate our analysis, in Section 3 we consider the optimal timing problem under a parametric market model with a non-traded underlying asset. This incomplete market setting, sometimes called the basis risk model, has been adopted for utility-based valuation for a number of applications, such as weather derivatives (Davis, 2001), commodities (Davis, 2006), credit derivatives (Leung et al, 2008;Sircar and Zariphopoulou, 2010;Jaimungal and Sigloch, 2010), real options (Henderson, 2007), and employee stock options (Henderson, 2005;Leung and Sircar, 2009a). With basis risk, the delayed purchase premium for a generic contingent claim under exponential utility involves the stochastic bracket between the market price and a density process, plus a quadratic penalization around a benchmark risk premium (see Theorem 7).…”

A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk

“…Utility based pricing has also been utilized by Bielecki and Jeanblanc [6], Sircar and Zariphopolou [43] and recently Jiao et al [27] [28] in an intensity based setting. Several authors have applied it in modeling of defaultable bonds where the problem remains one dimensional, see in particular Leung et al [35], Jaimungal and Sigloch [25], and Liang and Jiang [36]. In contrast, options subject to counterparty risk are a natural situation where two or more dimensions arise.…”

Incorporating Risk and Ambiguity Aversion Into a Hybrid Model of Default

“…Leung, Sircar, and Zariphopoulou (2008) recently introduced a unique structural model worthy of further mention. The firm’s stock price and its asset value are modeled as correlated geometric Brownian processes.…”