Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model

Abstract

This paper develops two novel methodologies for pricing and hedging European-style barrier option contracts under the jump to default extended constant elasticity of variance (JDCEV) model, namely: a stopping time approach based on the first passage time densities of the underlying asset price process through the barrier levels; and a static hedging portfolio approach in which the barrier option is replicated by a portfolio of plain-vanilla and binary options. In doing so, both valuation methodologies are extended to a more general set-up accommodating endogenous bankruptcy, timedependent barriers and the commonly observed stylized facts of a positive link between default and equity volatility and of a negative link between volatility and stock price. The two proposed numerical methods are shown to be accurate, easy to implement and efficient under both the JDCEV model and the nested constant elasticity of variance model.

Repeated Richardson extrapolation and static hedging of barrier options under the CEV model

“…6 For instance, Ballestra and Cecere (2015), Nunes (2009), and Ruas, Dias, and Nunes (2013) use the CEV model for pricing and hedging American-style options. Chung et al (2013aChung et al ( , 2013b, Dias, Nunes, and Ruas (2015), Nunes et al (2015), and Tsai (2014) use the CEV model for pricing and hedging barrier options. 7 For β > 2, Emanuel and MacBeth (1982) report a second expression for the call price, denoted by C EM (S 0 , K, T, r, d, δ, β) = ( )…”

“…replication performance of UOCs, respectively, using the DEK, modified DEK, and repeated Richardson extrapolation of DEK and modified DEK methods under the CEV process even with an inverse leverage effect (i.e., with β > 2). The constellation of parameters used by Dias et al (2015 , Table 1) for pricing European-style barrier options is adopted to investigate these alternative methods of SHP, that is, S 0 = 100, K ∈ {105, 100, 95}, β ∈ {5, 3, 2, 1, 0}, T = 0.5 years, δS = 0.25 β 0 ( /2)−1 , r = 10%, d = 0, and U = 120. The CPU time (in seconds) of the 15 contracts is shown in the ultimate row of Table 3.…”

“…T A B L E 5 A comparison of four SHP methods for pricing European double barrier knock-out call options This table compares the four methods discussed in this paper for pricing European double barrier call options under the CEV model using the parameters configuration ofDias et al (2015, …”

Pricing Double Barrier Options on Homogeneous Diffusions: A Neumann Series of Bessel Functions Representation

“…More recently, [14] tackle the valuation of DBKO options (using the stopping time approach as well as the static hedging approach) under the so-called jump to default CEV (hereafter, JDCEV) model proposed by [7], which is known to be able to capture the empirical evidence of a positive correlation between default probabilities (or credit default swap spreads) and equity volatility. 1 Moreover, it nests the GBM and CEV models as special cases and, therefore, it also accommodates the aforementioned leverage effect and implied volatility skew stylized facts.…”

“…The importance of linking equity derivatives markets and credit markets has thus generated a new class of hybrid credit-equity models with the aim of pricing derivatives subject to the risk of default-for other applications of jump to default models, see, for instance, [32], [29], [28], [40], [34], [33], and the references contained therein. Moreover, the new algorithms recently provided by [13] for computing truncated and raw moments of a noncentral χ 2 random variable can be also used on the pricing of barrier options under the JDCEV model considered in [14].…”