A Mellin Transform Approach to the Pricing of Options with Default Risk

A Mellin transform approach to pricing barrier options under stochastic elasticity of variance

“…The model (1) also has been calibrated by Kim et al 5 for the pricing group parameters of European vanilla options. So, we inevitably use an ad-hoc reasonable choice of the parameter values for the experiment which have been used for numerical experiments in the previous literature of Yoon and Park 16 and Choi et al 7 Based on the order condition for 𝛿 and 𝜖, they are K = 100, B = 80, t = 0, T = 1, N = 1000, r = 0.02, 𝜎 = 0.3, 𝜌 = 0.2, m = 0, 𝜈 = 0.5, y 0 = 0.3, 𝛿 = 0.001, and 𝜖 = 0.006. The function f is chosen to be wide range of underlying prices.…”

“…The model (1) also has been calibrated by Kim et al$$$ {}^5 $$$ for the pricing group parameters of European vanilla options. So, we inevitably use an ad‐hoc reasonable choice of the parameter values for the experiment which have been used for numerical experiments in the previous literature of Yoon and Park 16 and Choi et al 7 Based on the order condition for $$$ \delta $$$ and $$$ \epsilon $$$, they are $$$ K=100 $$$, $$$ B=80 $$$, $$$ t=0 $$$, $$$ T=1 $$$, $$$ N=1000 $$$, $$$ r=0.02 $$$, $$$ \sigma =0.3 $$$, $$$ \rho =0.2 $$$, $$$ m=0 $$$, $$$ \nu =0.5 $$$, $$$ {y}_0=0.3 $$$, $$$ \delta =0.001 $$$, and …”

“…The formula is explicitly expressed by elementary functions without any integral terms that appear in Kim et al 5 There are also other works employing the Mellin transform to price options in the SEV model. We refer readers to Choi et al 7 for pricing European vanilla options with default risk and Seo and Kim 8 for the evaluation of equity‐linked‐annuity.…”