A nonlinear Kolmogorov equation for stochastic functional delay differential equations with jumps

We consider a stochastic functional delay differential equation, namely an equation whose evolution depends on its past history as well as on its present state, driven by a pure diffusive component plus a pure jump Poisson compensated measure. We lift the problem in the infinite dimensional space of square integrable Lebesgue functions in order to show that its solution is an $L^2-$valued Markov process whose uniqueness can be shown under standard assumptions of locally Lipschitzianity and linear growth for the coefficients. Coupling the aforementioned equation with a standard backward differential equation, and deriving some ad hoc results concerning the Malliavin derivative for systems with memory, we are able to derive a non--linear Feynman--Kac representation theorem under mild assumptions of differentiability

Co-jumps and recursive preferences in portfolio choices

This paper investigates a multivariate, dynamic, continuous-time optimal consumption and portfolio allocation problem when the investor faces recursive utilities. The economy we are considering is described through both diffusion and discontinuities in the dynamics. We derive an approximated closed-form solution to optimal rules by exploiting standard dynamic programming techniques. Our findings are manifold. First, we obtain dynamic optimal weights, inversely proportional to volatility. Second, we show that both co-jumps frequency and intensity play a crucial role, as they considerably limit potential losses in the investors’ wealth. Third, we prove that jumps in precision reinforce the effect of jumps in price, further reducing optimal allocation. Finally, we highlight how co-jumps may influence investors’ choices regarding intertemporal consumption

Estimating the Counterparty Risk Exposure by using the Brownian Motion Local Time

In recent years, the counterparty credit risk measure, namely the default risk in \emph{Over The Counter} (OTC) derivatives contracts, has received great attention by banking regulators, specifically within the frameworks of \emph{Basel II} and \emph{Basel III.} More explicitly, to obtain the related risk figures, one has first obliged to compute intermediate output functionals related to the \emph{Mark-to-Market} (MtM) position at a given time $t \in [0, T],$ T being a positive, and finite, time horizon. The latter implies an enormous amount of computational effort is needed, with related highly time consuming procedures to be carried out, turning out into significant costs. To overcome latter issue, we propose a smart exploitation of the properties of the (local) time spent by the Brownian motion close to a given value

A Unified Approach to xVA with CSA Discounting and Initial Margin

In this paper we extend the existing literature on xVA along three directions. First, we extend existing BSDE-based xVA frameworks to include initial margin by following the approach of Cr\ue9pey (2015a) and Cr\ue9pey (2015b). Next, we solve the consistency problem that arises when the front- office desk of the bank uses trade-specific discount curves that differ from the discount curve adopted by the xVA desk. Finally, we address the existence of multiple aggregation levels for contingent claims in the portfolio between the bank and the counterparty by providing suitable extensions of our proposed single-claim xVA framework

Options on constant proportion portfolio insurance with guaranteed minimum equity exposure

In the present paper we study a new exotic option offering participation in a dynamic asset allocation strategy, which is an extension of the well-knownConstant Proportion Portfolio Insurance(CPPI) strategy. Our novel approach consists in assuming that the percentage of wealth invested in stocks cannot go under a fixed level, calledguaranteed minimum equity exposure(GMEE). In particular, our proposal ensures to overcome the so-calledcash-inrisk, typically related to a standard CPPI technique, simultaneously guaranteeing the equity market participation. We look deeper into the valuation of call and put options linked to this new CPPI-GMEE strategy. A particular attention is devoted to the analysis of key parameters' value as to gain a better understanding of the sensitivities of the option prices, when changing, for example, the embedded guarantee level. To show the effectiveness of our proposal we provide a detailed computational analysis within the Heston-Vasicek framework, numerically comparing the evaluation of the price of European plain vanilla options when the underlying is either a purely risky asset, a standard CPPI portfolio and a CPPI with GMEE

Time‐invariant portfolio strategies in structured products with guaranteed minimum equity exposure

We introduce a new exotic option to be used within structured products to address a key disadvantage of standard time-invariant portfolio protection: the well-known cash-lock risk. Our approach suggests enriching the framework by including a threshold in the allocation mechanism so that a guaranteed minimum equity exposure (GMEE) is ensured at any point in time. To be able to offer such a solution still with hard capital protection, we apply an option-based structure with a dynamic allocation logic as underlying. We provide an in-depth analysis of the prices of such new exotic options, assuming a Heston–Vasicek-type financial market model, and compare our results with other options used within structured products. Our approach represents an interesting alternative for investors aiming at downsizing protection via time-invariant portfolio protection strategies, meanwhile being also afraid to experience a cash-lock event triggered by market turmoils

AN INTERVAL OF NO-ARBITRAGE PRICES FOR AMERICAN CONTINGENT CLAIMS IN INCOMPLETE MARKETS

In this paper we establish an arbitrage-free prices interval for in incomplete financial markets. Such an incompleteness derives from considering uncertain volatility. We use the notion of G-expectation, under which the corresponding canonical path is a G-Browian motion, and the related stochastic calculus on suitable stopping time intervals, in a standard financial market characterized by a risk-less asset and one risky stock

Betting on bitcoin: a profitable trading between directional and shielding strategies

In this paper, we come up with an original trading strategy on Bitcoins. The methodology we propose is profit-oriented, and it is based on buying or selling the so-called Contracts for Difference, so that the investor’s gain, assessed at a given future time t, is obtained as the difference between the predicted Bitcoin price and an apt threshold. Starting from some empirical findings, and passing through the specification of a suitable theoretical model for the Bitcoin price process, we are able to provide possible investment scenarios, thanks to the use of a Recurrent Neural Network with a Long Short-Term Memory for predicting purposes

Counterparty Credit Risk evaluation for Accumulator derivatives: the Brownian Local Time approach

In this paper we aim at exploiting the properties of the Brownian Local Time to estimate the Counterparty Credit Risk for a specific class of financial derivatives, i.e. the so called Accumulator derivatives , within a Black and Scholes-type market. The comparison with the results obtained by made use of a standard Monte Carlo approach, clearly shows the superiority of our proposal, which runs in smaller execution times and with better estimation accuracy

Mortality and pulmonary complications in patients undergoing surgery with perioperative SARS-CoV-2 infection: an international cohort study

Background: The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods: This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings: This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (74·0%) had emergency surgery and 280 (24·8%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (26·1%) patients. 30-day mortality was 23·8% (268 of 1128). Pulmonary complications occurred in 577 (51·2%) of 1128 patients; 30-day mortality in these patients was 38·0% (219 of 577), accounting for 81·7% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 1·75 [95% CI 1·28–2·40], p\textless0·0001), age 70 years or older versus younger than 70 years (2·30 [1·65–3·22], p\textless0·0001), American Society of Anesthesiologists grades 3–5 versus grades 1–2 (2·35 [1·57–3·53], p\textless0·0001), malignant versus benign or obstetric diagnosis (1·55 [1·01–2·39], p=0·046), emergency versus elective surgery (1·67 [1·06–2·63], p=0·026), and major versus minor surgery (1·52 [1·01–2·31], p=0·047). Interpretation: Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding: National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research