Algorithms for improving the efficiency of CEV, CIR and JDCEV option pricing models - Sousa, Pedro Filipe Botelho Negrão de (2017)
The non-central chi-square distribution function has extensive use in the field of Mathematical Finance. To a great extent, this is due to its involvement in the constant elasticity of variance (hereafter, CEV) option pricing model of Cox (1975), in the term structure of interest rates model of Cox et al. (1985a) (hereafter, CIR), and the jump to default extended CEV (hereafter, JDCEV) framework of Carr and Linetsky (2006). Efficient computation methods are required to rapidly price complex contracts and calibrate financial models. The processes with several parameters, like the CEV or JDCEV models that we will address are examples of where this is important, since in this case the pricing problem (for many strikes) is used inside an optimization method. With this work we intend to test recent developments concerning the efficient computation of the non-central chi-square distribution function in the context of these option pricing models. We will give particular emphasis to the recent developments presented in the work of Gil et al. (2012), Gil et al. (2013), Dias and Nunes (2014), and Gil et al. (2015). For each option pricing model, we will define reference data-sets compatible with the most common combination of values used in pricing practice, following a framework that is similar to the one presented in Larguinho et al. (2013). We will conclude by offering novel analytical solutions for the JDCEV delta hedge ratios for the recovery parts of the put.