Recovering greeks from sensitivities

24 Pages Posted: 2 Feb 2020 Last revised: 2 Oct 2020

Date Written: September 30, 2020

Abstract

We present a model-independent method for calculating delta, vega and rho based on a comparison of the sensitivities of any derivative payoff with those of its underlying observables. In doing so, we obtain generic definitions for these greeks with an intuitive geometric interpretation. By means of examples, we show how our definitions reduce to standard formulae for familiar special cases. For pure delta hedging of quanto options, we show that the standard formula for delta should be corrected to account for the convexity adjustment in the underlying forward. Finally, by applying the technique to physical and cash-settled swaptions, we illustrate that a systematic approach for calculating delta and vega ensures that contributions from the annuity are captured in a consistent manner.

Keywords: Options, greeks, delta, vega, delta-hedging, adjoint algorithmic differentiation

Suggested Citation

Goyder, Russell and Goodvin, Glen and Gibbs, Mark, Recovering greeks from sensitivities (September 30, 2020). Available at SSRN: https://ssrn.com/abstract=3506868 or http://dx.doi.org/10.2139/ssrn.3506868

Russell Goyder (Contact Author)

FINCAD Corporation ( email )

Central City, Suite 1750
13450 102nd Ave
Surrey, British Columbia V3T 5X3
Canada

HOME PAGE: http://www.fincad.com

Glen Goodvin

FINCAD ( email )

Central City, Suite 1750
13450 102nd Ave
Surrey, British Columbia V3T 5X3
Canada

Mark Gibbs

Gibbs Consulting ( email )

PO Box 244
Cobble Hill, British Columbia V0R 1L0
Canada

HOME PAGE: http://gibbsconsulting.ca

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