Risk sensitivities, also referred to as Greeks, are the measure of a financial instrument’s value reaction to changes in underlying factors. The value of a financial instrument is impacted by many factors, such as interest rate, stock price, implied volatility, time, etc. Sensitivities are risk measures that are more important than fair values.
Risk sensitivities or Greeks are vital for risk management. They can help financial market participants isolating risk, hedging risk and explaining profit & loss. This presentation gives certain practical insights onto this topic.
Delta is a first-order Greek that measures the value change of a financial instrument with respect to changes in the underlying asset price.
Vega is a first-order Greek that measures the value change of a financial instrument with respect to changes in the underlying implied volatility.
Gamma is a second order Greek that measures the value change of a financial instrument with respect to changes in the underlying price.
Theta is a first order Greek that measures the value change of a financial instrument with respect to time.
Curvature is a new risk measure introduced by Basel FRTB. It is a risk measure that captures the incremental risk not captured by the delta risk of price changes in the value of an option.
The objective of hedging is to have a lower price volatility that eliminate both downside risk (loss) and upside profit. It is a double-edged sword. The benefit of a broker or investment bank comes from spread rather than market movement. Thus it is better to hedge all risk. Delta is normally hedged. Vega can be hedged by using options. Gamma is hardly hedged in real world.
Hypothetic P&L is the P&L that is purely driven by market movement. Hypothetic P&L is calculated by revaluing a position held at the end of the previous day using the market data at the end of the current day,
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