The Greeks and Hedging Explained by Peter Leoni

By Peter Leoni

A sensible consultant to easy and intermediate hedging strategies for investors, structerers and hazard administration quants. This publication fills a niche for a technical yet no longer impenetrable consultant to hedging strategies, and the 'Greek' (Theta, Vega, Rho and Lambda) -parameters that characterize the sensitivity of derivatives prices.

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There is no other reference available and there is a substantial model risk involved. By using the Black–Scholes valuation and our own assessment of the volatility, one is in effect exposed to model risks as well. If, however, the option market by itself is liquid and quotes are available for those instruments, the valuation shifts to the MtM. 6 P&L The income or profit and loss (P&L) statement indicates the net income of the operations. Typically, the reported P&L are gross numbers that don’t take into account operating expenses or taxes.

Once the data has been generated, one can try to look back at it and estimate the realised volatility. Because of the finite nature of the dataset, it will deviate slightly from the imposed volatility. However, it will be quite close. 5 Implied Volatility Another, more market-related, volatility concept is the implied volatility. This takes everything to the next step, taking into account the options market. Up till now, we only talked about the underlying stock and its behaviour, in particular the fluctuations in the past, present and future.

This means that the implied volatility does not imply anything for the future [54]. We will elaborate more on this in later chapters. There are extensive studies on comparing the realised or historical volatility to the implied volatility. Typically there is a risk premium in the implied volatility. For a good analysis, we refer to [137, 82]. 6 Hedging Volatility A last question one can ask oneself is what volatility to use in the hedging procedure dictated by the Black–Scholes model. It may seem like a stupid question, because it has already been answered by the implied volatility.

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