• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.299-313
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• 2015

In this paper, we show the effectiveness of copulas by comparing the correlation of market data of year 2010 with those of years 2006-2009 and investigate copula functions as pricing methods of digital and rainbow options through real market data. We propose an accurate method of pricing rainbow options by using the correlation coefficients obtained from the copula functions depending on strike prices between assetes instead of simple traditional correlation coefficients.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.93-106
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• 2021

In this paper, an efficient hybrid numerical method for solving two-asset option pricing problem is presented based on the Crank-Nicolson and the radial basis function methods. For this purpose, the two-asset Black-Scholes partial differential equation is considered. Also, the convergence of the proposed method are proved and implementation of the proposed hybrid method is specifically studied on Exchange and Call on maximum Rainbow options. In addition, this method is compared to the explicit finite difference method as the benchmark and the results show that the proposed method can achieve a noticeably higher accuracy than the benchmark method at a similar computational time. Furthermore, the stability of the proposed hybrid method is numerically proved by considering the effect of the time step size to the computational accuracy in solving these problems.

• Journal of Gastric Cancer
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• v.23 no.2
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• pp.289-302
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• 2023

Purpose: Liver metastasis (LM) is reported in approximately 40% of patients with advanced/metastatic gastric/gastroesophageal junction adenocarcinoma (metastatic esophagogastric adenocarcinoma; mGEA) and is associated with a worse prognosis. This post-hoc analysis from the RAINBOW trial reported the efficacy, safety, and biomarker outcomes of ramucirumab and paclitaxel combination treatment (RAM+PAC) in patients with (LM+) and without (LM-) LM at baseline. Materials and Methods: Patients (n=665) were randomly assigned on a 1:1 basis to receive either RAM+PAC (LM+: 150, LM-: 180) or placebo and paclitaxel (PL+PAC) (LM+: 138, LM-: 197). The overall survival (OS) and progression-free survival (PFS) were evaluated using stratified Kaplan-Meier and Cox regression models. The correlation of dichotomized biomarkers (VEGF-C, D; VEGFR-1,2) with efficacy in the LM+ versus LM- subgroups was analyzed using the Cox regression model with reported interaction P-values. Results: The presence of LM was associated with earlier progression than those without LM, particularly in patients receiving PL+PAC (hazard ratio [HR], 1.68). RAM+PAC treatment improved OS and PFS irrespective of LM status but showed greater improvement in LM+ than that in LM- (OS HR, 0.71 [LM+] vs. 0.88 [LM-]; PFS HR, 0.47 [LM+] vs. 0.76 [LM-]). Treatment-emergent adverse events were similar between patients with and without LM. No predictive relationship was observed between biomarker levels (VEGF-C, D; VEGFR-1,2) and efficacy outcome (OS, PFS) (all interaction P-values >0.05). Conclusions: RAM provided a significant benefit, irrespective of LM status; however, its effect was numerically stronger in patients with LM. Therefore, RAM+PAC is a clinically meaningful therapeutic option for patients with mGEA and LM.