Risk Measurement for a Bank’s Digital Call Hedged as a Call Spread

Summary

The document raises a risk measurement question for a bank that sells a digital call to a client but represents or hedges the position internally as a call spread around the strike. The trader believes the spread may smooth hedging, while the bank still faces the digital option’s contingent payoff to the client.

The issue is whether risk management should assess the contractual digital obligation, the call spread used in the trader’s book, or both. The document gives no proposed framework, quantitative analysis, or answer. It highlights a distinction between external payoff exposure and internal hedge representation, leaving open how to measure residual risk, model basis, and hedge performance around the strike.

Key ideas

• The bank’s client-facing digital option has a discontinuous payoff at its strike.
• The trader uses a call spread as a representation or hedge to smooth position management.
• Risk measurement must account for the relationship between the contractual obligation and the booked hedge.
• The document poses the issue but provides no risk methodology or resolution.

Tags

# Risk management for Digital Option at large Bank


# Risk management for Digital Option at large Bank












Say, an investment bank sell Digital Call Option to its client at strike 100. But trader at the bank want to book the deal with a call spread at 99/100 (price&hedge Digital Option like price&hedge a call spread) because trader believe that it will help smoothing hedging.

How should risk manager at the bank measure the risk?

- a digital option as it is an actual contingent obligation?

- or a call spread as it is what trader book the deal?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.