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Derivatives Algorithms provides a unique expert overview of the abstractions and coding methods which support real-world derivatives trading. Written by an industry professional with extensive experience in large-scale trading operations, it describes the fundamentals of library code structure, and innovative advanced solutions to thorny issues in implementation. For the reader already familiar with C++ and arbitrage-free pricing, the book offers an invaluable glimpse of how they combine on an industrial scale. Topics range from interface design through code generation to the protocols that support ever more complex trades and models.Sample Chapter(s)Chapter 1: Introduction (104 KB)Contents: PrinciplesTypes and InterfacesVector and Matrix ComputationsPersistence and MemoryTesting FrameworkFurther MathsSchedulesIndicesPricing ProtocolsStandardized TradesCurvesModelsSemianalytic PricersRiskAdditional CodeReadership: Practicing quants, financial IT professionals and financial engineers.

Derivatives Algorithms provides a unique expert overview of the abstractions and coding methods which support real-world derivatives trading. Written by an industry professional with extensive experience in large-scale trading operations, it describes the fundamentals of library code structure, and innovative advanced solutions to thorny issues in implementation. For the reader already familiar with C++ and arbitrage-free pricing, the book offers an invaluable glimpse of how they combine on an industrial scale. Topics range from interface design through code generation to the protocols that support ever more complex trades and models.

Key Features:Unique focus on algorithms and implementationConsists of fundamentals as well as very advanced techniquesProvides a large-scale overview of the real work of quants.

Background Although the Barcelona Clinic Liver Cancer (BCLC) staging system has been largely adopted in clinical practice, recent studies have questioned the prognostic stratification of this classification schema, as well as the proposed treatment allocation of patients with a single large tumor. Methods Patients who underwent curative-intent hepatectomy for histologically proven hepatocellular carcinoma (HCC) between 1998 and 2017 were identified using an international multi-institutional database. Overall survival (OS) among patients with BCLC stage 0, A, and B was examined. Patients with a single large tumor were classified as BCLC stage A1 and were independently assessed. Results Among 814 patients, 68 (8.4%) were BCLC-0, 310 (38.1%) were BCLC-A, 279 (34.3%) were BCLC-A1, and 157 (19.3%) were BCLC-B. Five-year OS among patients with BCLC stage 0, A, A1, and B HCC was 86.2%, 69.0%, 56.9%, and 49.9%, respectively ( p  < 0.001). Among patients with very early- and early-stage HCC (BCLC 0, A, and A1), patients with BCLC stage A1 had the worst OS ( p  = 0.0016). No difference in survival was noted among patients undergoing surgery for BCLC stage A1 and B HCC (5-year OS: 56.9% vs. 49.9%; p  = 0.259) even after adjusting for competing factors (hazard ratio 0.83, 95% confidence interval 0.54–1.28; p  = 0.40). Conclusion Prognosis following liver resection among patients with BCLC-A1 HCC was similar to patients presenting with BCLC-B tumors. Surgery provided acceptable long-term outcomes among select patients with BCLC-B HCC. Designation into BCLC stage B should not be considered an a priori contraindication to surgery.

BackgroundSeveral investigators have advocated for extending the Barcelona Clinic Liver Cancer (BCLC) resection criteria to select patients with BCLC-B and even BCLC-C hepatocellular carcinoma (HCC). The objective of the current study was to define the outcomes and recurrence patterns after resection within and beyond the current resection criteria.Patients and MethodsPatients who underwent resection for HCC within (i.e., BCLC 0/A) and beyond (i.e. BCLC B/C) the current resection criteria between 2005 and 2017 were identified from an international multi-institutional database. Overall survival (OS), disease-free survival (DFS), as well as patterns of recurrence of patients undergoing HCC resection within and beyond the BCLC guidelines were examined.ResultsAmong 756 patients, 602 (79.6%) patients were BCLC 0/A and 154 (20.4%) were BCLC B/C. Recurrences were mostly intrahepatic (within BCLC: 74.3% versus beyond BCLC: 70.8%, p = 0.80), with BCLC B/C patients more often having multiple tumors at relapse (69.6% versus 49.4%, p = 0.001) and higher rates of early (< 2 years) recurrence (88.0% versus 75.5%, p = 0.011). During the first postoperative year, annual recurrence was 38.3% and 21.3% among BCLC B/C and BCLC 0/A patients, respectively; 5-year OS among BCLC 0/A and BCLC B/C patients was 76.9% versus 51.6% (p = 0.003). On multivariable analysis, only a-fetoprotein (AFP) > 400 ng/mL (HR = 1.84, 95% CI 1.07–3.15) and R1 resection (HR = 2.36, 95% CI 1.32–4.23) were associated with higher risk of recurrence among BCLC B/C patients.ConclusionsSurgery can provide acceptable outcomes among select patients with BCLC B/C HCC. The data emphasize the need to further refine the BCLC treatment algorithm as well as highlight the need for surveillance protocols with a particular focus on the liver, especially for patients undergoing resection outside the BCLC criteria.

Background The impact of tumor burden score (TBS) on conditional survival (CS) among patients undergoing curative-intent resection of hepatocellular carcinoma (HCC) has not been examined to date. Methods Patients who underwent liver resection of HCC between 2000 and 2017 were identified from a multi-institutional database. The impact of TBS and other clinicopathologic factors on 3-year conditional survival (CS 3 ) was examined. Results Among 1,040 patients, 263 (25.3%) patients had low TBS, 668 (64.2%) had medium TBS and 109 (10.5%) had high TBS. TBS was strongly associated with OS; 5-year OS was 39.0% among patients with high TBS compared with 61.1% and 79.4% among patients with medium and low TBS, respectively ( p  < 0.001). While actuarial survival decreased as time elapsed from resection, CS increased over time irrespective of TBS. The largest differences between 3-year actuarial survival and CS 3 were noted among patients with high TBS (5-years postoperatively; CS 3 : 78.7% vs. 3-year actuarial survival: 30.7%). The effect of adverse clinicopathologic factors including high TBS, poor/undifferentiated tumor grade, microvascular invasion, liver capsule involvement, and positive margins on prognosis decreased over time. Conclusions CS rates among patients who underwent resection for HCC increased as patients survived additional years, irrespective of TBS. CS estimates can be used to provide important dynamic information relative to the changing survival probability after resection of HCC.

Introduction Although a positive surgical margin is a known prognostic factor for recurrence, the optimal surgical margin width in the context of an R0 resection for early-stage hepatocellular carcinoma (HCC) is still debated. The aim of the current study was to examine the impact of wide ( >  1 cm) versus narrow (< 1 cm) surgical margin status on the incidence and recurrence patterns among patients with T1 HCC undergoing an R0 hepatectomy. Methods Between 1998 and 2017, patients with T1 HCC who underwent R0 hepatectomy for stage T1 HCC were identified using an international multi-institutional database. Recurrence-free survival (RFS) was estimated, and recurrence patterns were examined based on whether patients had a wide versus narrow resection margins. Results Among 404 patients, median patient age was 66 years (IQR: 58–73). Most patients ( n  = 326, 80.7%) had surgical margin < 1 cm, while 78 (19.3%) patients had a >  1 cm margin. The majority of patients had early recurrences (< 24 months) in both margin width groups (< 1 cm: 70.3% vs >  1 cm: 85.7%, p  = 0.141); recurrence site was mostly intrahepatic (< 1 cm: 77% vs >  1 cm: 61.9%, p  = 0.169). The 1-, 3-, and 5-year RFS among patients with margin < 1 cm were 77%, 48.9%, and 35.3% versus 81.7%, 65.8%, and 60.7% for patients with margin >  1 cm, respectively ( p  = 0.02). Among patients undergoing anatomic resection, resection margin did not impact RFS (3-year RFS: < 1 cm: 49.2% vs >  1 cm: 58.9%, p  = 0.169), whereas in the non-anatomic resection group, margin width >  1 cm was associated with a better 3-year RFS compared to margin < 1 cm (86.7% vs 47.3%, p  = 0.017). On multivariable analysis, margin >  1 cm remained protective against recurrence (HR = 0.50, 95%CI 0.28–0.89), whereas Child-Pugh B (HR = 2.13, 95%CI 1.09–4.15), AFP >  20 ng/mL (HR = 1.71, 95%CI 1.18–2.48), and presence of microscopic lymphovascular invasion (HR = 1.48, 95%CI 1.01–2.18) were associated with a higher hazard of recurrence. Conclusion Resection margins >  1 cm predicted better RFS among patients undergoing R0 hepatectomy for T1 HCC, especially small (< 5 cm) HCC. Although resection margin width did not influence outcomes after anatomic resection, wider margins were more important among patients undergoing non-anatomic liver resections.