Log Student’s <italic>t</italic>-distribution-based option sensitivities: Greeks for the Gosset formulae

European options can be priced when returns follow a log Student’s <italic>t</italic>-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Student’s <italic>t</italic>-distribution a Gosset approach, in honour of W.S. Gosset. In this paper, we compare the Greeks for Gosset and Black--Scholes formulae and we discuss implementation. The <italic>t</italic>-distribution requires a shape parameter <inline-formula id="ILM0001"> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rquf_a_744087_o_ilm0001.gif"/> </inline-formula> to match the ‘fat tails’ of the observed log returns. For large <inline-formula id="ILM0002"> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rquf_a_744087_o_ilm0002.gif"/> </inline-formula>, the Gosset and Black--Scholes formulae are equivalent. The Gosset formula removes the requirement that the volatility be known, and in this sense can be viewed as an extension of the Black--Scholes formula.