Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Increasing Utilization of US Electric Grids via Smart Technologies: Integration of Load Management, Real Time Pricing, Renewables, EVs and Smart Grid Sensors

Electric power grids throughout the world suffer from serious inefficiencies associated with under-utilization due to demand patterns, engineering design and load following approaches in use today. These grids consume much of the world’s energy and represent a large carbon footprint. From material utilization perspectives significant hardware is manufactured and installed for this infrastructure often to be used at less than 20-40% of its operational capacity for most of its lifetime. These inefficiencies lead engineers to require additional grid support and conventional generation capacity additions when renewable technologies (such as solar and wind) and electric vehicles are to be added to the utility demand/supply mix. Using actual data from the PJM [PJM 2009] the work shows that consumer load management, real time price signals, sensors and intelligent demand/supply control offer a compelling path forward to increase the efficient utilization and carbon footprint reduction of the world’s grids. Underutilization factors from many distribution companies indicate that distribution feeders are often operated at only 70-80% of their peak capacity for a few hours per year, and on average are loaded to less than 30-40% of their capability. By creating strong societal connections between consumers and energy providers technology can radically change this situation. Intelligent deployment of smart sensors, smart electric vehicles, consumer-based load management technology very high saturations of intermittent renewable energy supplies can be effectively controlled and dispatched to increase the levels of utilization of existing utility distribution, substation, transmission, and generation equipment. The strengthening of these technology, society and consumer relationships requires rapid dissemination of knowledge (real time prices, costs & benefit sharing, demand response requirements) in order to incentivize behaviors that can increase the effective use of technological equipment that represents one of the largest capital assets modern society has created.

Immediate or deferred androgen deprivation for patients with prostate cancer not suitable for local treatment with curative intent: European Organisation for Research and Treatment of Cancer (EORTC) Trial 30891

PURPOSE: This study (EORTC 30891) attempted to demonstrate equivalent overall survival in patients with localized prostate cancer not suitable for local curative treatment treated with immediate or deferred androgen ablation. PATIENTS AND METHODS: We randomly assigned 985 patients with newly diagnosed prostate cancer T0-4 N0-2 M0 to receive androgen deprivation either immediately (n = 493) or on symptomatic disease progression or occurrence of serious complications (n = 492). RESULTS: Baseline characteristics were well balanced in the two groups. Median age was 73 years (range, 52 to 81). At a median follow-up of 7.8 years, 541 of 985 patients had died, mostly of prostate cancer (n = 193) or cardiovascular disease (n = 185). The overall survival hazard ratio was 1.25 (95% CI, 1.05 to 1.48; noninferiority P > .1) favoring immediate treatment, seemingly due to fewer deaths of nonprostatic cancer causes (P = .06). The time from randomization to progression of hormone refractory disease did not differ significantly, nor did prostate-cancer specific survival. The median time to the start of deferred treatment after study entry was 7 years. In this group 126 patients (25.6%) died without ever needing treatment (44% of the deaths in this arm). CONCLUSION: Immediate androgen deprivation resulted in a modest but statistically significant increase in overall survival but no significant difference in prostate cancer mortality or symptom-free survival. This must be weighed on an individual basis against the adverse effects of life-long androgen deprivation, which may be avoided in a substantial number of patients with a deferred treatment policy.

Integrating Pricing and Inventory Control: Is it Worth the Effort?

In this paper we first show that the gains achievable by integrating pricing and inventory control are usually small for classical demand functions. We then introduce reference price models and demonstrate that for this class of demand functions the benefits of integration with inventory control are substantially increased due to the price dynamics. We also provide some analytical results for this more complex model. We thus conclude that integrated pricing/inventory models could repeat the success of revenue management in practice if reference price effects are included in the demand model and the properties of this new model are better understood.

The Pricing Discount for Limited Liquidity: Evidence from SWX Swiss Exchange and the Nasdaq

We investigate the pricing discount for limited liquidity. Unlike previous studies that have examined the relation between histroical returns and liquidity, ours looks directly at current stock prices. This approach requires less data and yields up-to-date information about limited liquidity discounts. We analyze data from the Swiss exchange and the Nasdaq during 1995-2001, and find a statistically and economically significant price-liquidity relation in both markets. We test the robustness of that relation with a procedure that does not rely on specific distributional assumptions. Our findings are unaffected. Accordingly, the discount suffered by the least liquid securities is about 30%.

The pricing of equity offerings

Examination of 1,600 seasoned equity offerings reveals little evidence that underwriters systematically set offer prices below the market price on the major exchanges, though they may do so for NASDAQ issues. Quick round-trip transactions in seasoned offerings are not profitable, but subscribing to an offering and holding the stock for 30 days seems to be very profitable, especially in the NASDAQ market. In addition to seasoned offerings, we analyze 250 issues of new classes of preferred stock. These issues are not underpriced.

Differences in Time to Disease Progression Do Not Predict for Cancer-specific Survival in Patients Receiving Immediate or Deferred Androgen-deprivation Therapy for Prostate Cancer: Final Results of EORTC Randomized Trial 30891 with 12 Years of Follow-up

BACKGROUND Trials assessing the benefit of immediate androgen-deprivation therapy (ADT) for treating prostate cancer (PCa) have often done so based on differences in detectable prostate-specific antigen (PSA) relapse or metastatic disease rates at a specific time after randomization. OBJECTIVE Based on the long-term results of European Organization for Research and Treatment of Cancer (EORTC) trial 30891, we questioned if differences in time to progression predict for survival differences. DESIGN, SETTING, AND PARTICIPANTS EORTC trial 30891 compared immediate ADT (n=492) with orchiectomy or luteinizing hormone-releasing hormone analog with deferred ADT (n=493) initiated upon symptomatic disease progression or life-threatening complications in randomly assigned T0-4 N0-2 M0 PCa patients. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS Time to first objective progression (documented metastases, ureteric obstruction, not PSA rise) and time to objective castration-resistant progressive disease were compared as well as PCa mortality and overall survival. RESULTS AND LIMITATIONS After a median of 12.8 yr, 769 of the 985 patients had died (78%), 269 of PCa (27%). For patients receiving deferred ADT, the overall treatment time was 31% of that for patients on immediate ADT. Deferred ADT was significantly worse than immediate ADT for time to first objective disease progression (p<0.0001; 10-yr progression rates 42% vs 30%). However, time to objective castration-resistant disease after deferred ADT did not differ significantly (p=0.42) from that after immediate ADT. In addition, PCa mortality did not differ significantly, except in patients with aggressive PCa resulting in death within 3-5 yr after diagnosis. Deferred ADT was inferior to immediate ADT in terms of overall survival (hazard ratio: 1.21; 95% confidence interval, 1.05-1.39; p [noninferiority]=0.72, p [difference] = 0.0085). CONCLUSIONS This study shows that if hormonal manipulation is used at different times during the disease course, differences in time to first disease progression cannot predict differences in disease-specific survival. A deferred ADT policy may substantially reduce the time on treatment, but it is not suitable for patients with rapidly progressing disease.

Restrictive deferred hydration combined with preemptive norepinephrine infusion during radical cystectomy reduces postoperative complications and hospitalization time: a randomized clinical trial.

BACKGROUND Anesthetics and neuraxial anesthesia commonly result in vasodilation/hypotension. Norepinephrine counteracts this effect and thus allows for decreased intraoperative hydration. The authors investigated whether this approach could result in reduced postoperative complication rate. METHODS In this single-center, double-blind, randomized, superiority trial, 166 patients undergoing radical cystectomy and urinary diversion were equally allocated to receive 1 ml·kg·h of balanced Ringer's solution until the end of cystectomy and then 3 ml·kg·h until the end of surgery combined with preemptive norepinephrine infusion at an initial rate of 2 µg·kg·h (low-volume group; n = 83) or 6 ml·kg·h of balanced Ringer's solution throughout surgery (control group; n = 83). Primary outcome was the in-hospital complication rate. Secondary outcomes were hospitalization time, and 90-day mortality. RESULTS In-hospital complications occurred in 43 of 83 patients (52%) in the low-volume group and in 61 of 83 (73%) in the control group (relative risk, 0.70; 95% CI, 0.55-0.88; P = 0.006). The rates of gastrointestinal and cardiac complications were lower in the low-volume group than in the control group (5 [6%] vs. 31 [37%]; relative risk, 0.16; 95% CI, 0.07-0.39; P < 0.0001 and 17 [20%] vs. 39 [48%], relative risk, 0.43; 95% CI, 0.26-0.60; P = 0.0003, respectively). The median hospitalization time was 15 days [range, 11, 27d] in the low-volume group and 17 days [11, 95d] in the control group (P = 0.02). The 90-day mortality was 0% in the low-volume group and 4.8% in the control group (P = 0.12). CONCLUSION A restrictive-deferred hydration combined with preemptive norepinephrine infusion during radical cystectomy and urinary diversion significantly reduced the postoperative complication rate and hospitalization time.