EQUITY TO CREDIT
Equity-to-Credit is the new form of volatility arbitrage. Credit risk (through the probability of the underlying equity jumping to zero) adds a component to option premium that cannot be financed by the usual rebalancing of the delta hedge issuing from the Black-Scholes-Merton model. Another hedging instrument has to be held and continuously traded in order to hedge the jump to default. Jointly inferring the Brownian volatility and the hazard rate from the market data of instruments sensitive both to volatility and credit risk (equity options, CDS) and computing the composite dynamic hedging strategy are the new rule of volatility arbitrage.
THE EQUITY-TO-CREDIT PARADIGM
The equity-to-credit paradigm is born from the recognition that credit dependent instruments, starting with standard corporate bonds, have an embedded equity component which results from the high correlation between the credit standing of an issuer and its stock price. With corporate default of big companies looming large in the last few years, investors have been stunned by the collapse of the famed bond floor of convertible bonds. It is now well recognized that the credit component must be hedged with other standard instruments such as CDS or out of the money puts. More generally, equity and credit instruments should be priced and hedged in a unique consistent framework, which is the essence of the equity-to-credit paradigm.
This creates both institutional and technical problems for market participants. Banks have traditionally traded their equity and credit portfolios in separate divisions which cannot cross-hedge their related exposures. Slowly and gradually, they are understanding that they need to merge the various desks which deal with the same issuer.
Hedge funds have taken advantage of the institutional rigidity of banks; they have been the first to benefit from this new paradigm by investing in strategies which aim to arbitrage inconsistencies between the credit and the equity markets. But as more money is flowing into these strategies, obvious opportunities disappear and accurate modelling becomes essential. Traders have so far relied on software and models which are good at pricing one family of instruments but fail to deal consistently with the entire equity-to-credit spectrum. This is an issue for both pre-trade analysis and risk management.
SOLVING THE EQUITY-TO-CREDIT PROBLEM
The Equity-to-Credit problem, as we understand it and handle it, is the problem of pricing and hedging of single name equity derivatives and credit derivatives when the issuer of the underlying equity is subject to default (or credit risk). Posing the problem means specifying the stochastic process followed by the underlying equity (typically, it is a jump-diffusion process where the diffusion, or Brownian component, admits of stochastic volatility and the jump component is a sum of Poisson jump processes with stochastic intensity and jump sizes, notable among which is the jump to default).