# Using Options on Greeks as Liquidity Protection

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Using options on Greeks as liquidity protection

David Bakstein and Sam Howison* *Mathematical Finance Group, University of Oxford, Mathematical Institute, 24–29 St. Giles’, Oxford OXI 3LB, UK. Tel. 44 (0)1865 270500; Fax. 44 (0)1865 270515; E-mail: howison@maths.ox.ac.uk Received: 17th April, 2003

David Bakstein completed his doctorate at Oxford University in 2002, on models for illiquid markets. He is now working on derivatives at Commerzbank. Sam Howison is the leader of Oxford University’s mathematical ﬁnance research group and Director of the Nomura Centre for Quantitative Finance in the mathematics department there. He has written numerous papers and several books on mathematical modelling in ﬁnance.

Practical applications Liquidity, or more usually the lack of it, can be a major problem for anybody hedging a derivatives position. This paper proposes a class of contracts that delivers ‘prepackaged’ liquidity to hedge exposures such as Gamma risk, enabling the contract holder to insure against liquidity risk, and the writer to generate premium income against exposures elsewhere in their portfolio.

Abstract In this paper we suggest derivative contracts related to the Greeks of options; we show how to value them and how they can be used to manage the risk of a portfolio of derivatives. Certain types of these options are described, namely those related to the Delta and Gamma, which can be regarded as a form of insurance against liquidity holes and transaction costs for the writer of the contract representing the underlying.

INTRODUCTION In the ﬁnancial literature and practice the sensitivities of portfolios of derivatives with respect to parameters like the underlying spot prices or their volatilities are referred to as the Greeks. Mathematically, the latter are calculated as various partial derivatives of the portfolio value with respect to the parameters. Important ones are the Delta and the Gamma, the ﬁrst and second derivative with respect to the...