A convertible can be marked at market-implied volatility but hedged with a different volatility. That choice silently creates a directional or volatility view because delta and gamma depend on the volatility fed to the model. This note makes the choice explicit, connects it to Calamos’s bull and bear gamma structures, and uses shadow gamma to keep a credit-sensitive convertible from being mistaken for a pure long-vol trade.
Learning objectives. By the end of this note you should be able to:
- distinguish implied, model/hedge, and realised volatility in a delta-hedged trade;
- explain why hedging at a different volatility is economically an over- or under-hedge;
- construct bull and bear tilts from a neutral share count;
- use shadow gamma and credit-volatility interaction in a portfolio-risk discussion.
In this lesson
- Three volatilities, three jobs
- Hedging at what volatility?
- Bull and bear gamma tilts
- Shadow gamma and credit-volatility interaction
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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