Using Equity Options to Hedge Credit Risks

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Credit risk refers to the potential for financial loss if a borrower fails to meet their debt obligations, such as repaying a loan or bond. Credit risk assessment involves evaluating the likelihood of default, often using financial metrics, historical performance, and credit ratings. Effective management of credit risk includes diversifying portfolios, setting appropriate interest rates, requiring collateral, and using credit derivatives to hedge potential losses.

Using credit derivatives, such as credit default swaps, to manage credit risks is a common practice in the financial industry. Reference [1] proposed an innovative approach that uses equity derivatives to partially hedge credit risks. The author generalizes the Merton structural model, where a company’s equity is viewed as a call option on its assets. However, instead of using the total debt level as the default trigger, they propose an alternative positive default threshold where default is determined by the stock price’s initial crossing of this predefined level. The credit loss then resembles the payoff of a digital put option.

To hedge this digital option, the author suggests using equity options. He utilizes an optimization procedure to determine (1) which option or strike to select, (2) the optimal quantity of options to buy, and (3) whether this strategy offers any net benefit for the insurance company, considering the premium cost of these options.  The author pointed out,

This study develops a novel method for mitigating credit risk through the use of structured derivatives, focusing in particular on the use of European put options as a strategic hedging tool. Inspired by the work of Merton (1974), our approach introduces the concept of default triggered by the stock price S_T breaching a predefined barrier B. By establishing a distributional equivalence between an existing default model and P(S_T < B) for a given time T, we demonstrate the potential for reducing the necessary capital allocation for a projected loss X(T) by partially hedging with a European put option. We formulate and solve an optimization problem w.r.t. a specific risk measure to determine the optimal strike price for the option, and our numerical analysis confirms a reduction in the Solvency Capital Requirement (SCR) in markets with and without jumps. Our findings provide (insurance) companies with a pragmatic approach to mitigating losses while maintaining their current risk management framework.

This approach is innovative as it reduces reliance on credit derivatives, which are not always available. However, equity derivatives also may not be accessible. To address this issue the author proposes using an index option as a proxy hedge.

Moreover, while the methodology presupposes the availability of derivatives for listed, liquid companies, the idea can be extended to unlisted entities via correlated liquid indices, factoring in a “correlation error” to adjust the findings accordingly.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Constantin Siggelkow, Partial hedging in credit markets with structured derivatives: a quantitative approach using put options, Journal of Derivatives and Quantitative Studies, 2024

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