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The occurrence of acute myeloid leukemia (AML) within six months from a diagnosis of breast cancer (BC) is rarely reported in the literature, and it is associated with a poor prognosis. We report herein the case of a 40-year-old woman referred to our centre affected by BC and simultaneous AML. The patient proved refractory to first line therapy and achieved complete remission (CR) with a clofarabine-based regimen followed by allogeneic stem cell transplantation (ASCT). Both during salvage chemotherapy and after ASCT, the patient presented severe infectious complications ( acute cholecistytis and Nocardia pneumonia, respectively) treated with surgery, and currently she is alive in CR for both diseases after 29 months of follow-up. The case highlights the importance of a diagnostic assessment of any unexplained cytopenia in association with solid neoplasia under treatment, underlining the feasibility and priority of a timely treatment of the haematological neoplasm in order to achieve long-term survival.

The idea of this document is to provide the reader with an intuitive, yet rigorous and comprehensive introduction to the main tools in stochastic analysis required in Finance to understand the modern modelling, pricing and hedging techniques. The most important models (Brownian motion, arithmetic and geometric Brownian motion, mean-reverting models, stochastic and jump processes) are considered and their properties illustrated with the help of Matlab codes and videos. We would like to emphasize that this document is very much work in progress and we would like to encourage readers to get in touch with us with feedback, comments, suggestions for additions and, of course, corrections of typos. All of these will be gratefully acknowledged in the future releases of this document.

This paper is an introduction to the measurement of market risk in financial markets, with examples drawn mainly from commodity markets. In particular, we present the concept of VaR, its limits, the problems related to its estimation and backtesting. This is done at single asset and at portfolio level. Issues related to estimation error, measurement of portfolio risk contribution and how to cope with derivative positions are also considered. Other important issues like liquidity, operational and credit risk will not be dealt here. For a Gentle introduction to the measurement of counterparty credit risk see the companion paper by Ballotta, Fusai and Marena always available on the SSRN web site.

In this paper we introduce the reader to the basic tools for the computation of Counterparty Credit Risk such as Credit Value Adjustment and Debt Value Adjustment. We also present the effect of mitigating clauses, like netting and collateral, in reducing the credit exposure. Detailed numerical examples are presented with reference to commodity derivatives.

We present a joint Monte Carlo-Fourier transform sampling scheme for pricing derivative products under a Carr–Geman–Madan–Yor (CGMY) model (Carr et al. [Journal of Business, 75, 305–332, 2002]) exhibiting jumps of infinite activity and finite or infinite variation. The approach relies on numerical transform inversion with computable error estimates, which allow generating the unknown cumulative distribution function of the CGMY process increments at the desired accuracy level. We use this to generate samples and simulate the entire trajectory of the process without need of truncating the process small jumps. We illustrate the computational efficiency of the proposed method by comparing it to the existing methods in the literature on pricing a wide range of option contracts, including path-dependent univariate and multivariate products.

This paper proposes an asset allocation strategy for the risk management of the broad category of participating life insurance policies. The nature of the liability implied by these contracts allows us to treat them as options written on the reference portfolio backing the policy; consequently, the valuation approach is based on classical contingent claim theory. This leads to the identification of additional safety loadings against the risk of default implied by these contracts, and the setting up of suitable investment strategies aimed at minimizing this risk. The impact on the solvency requirements for the capital of the insurer of the proposed asset allocation strategy is analyzed by means of Monte Carlo techniques. Stress testing is considered as well with respect to the key risk factors of the model, such as the equity volatility and the market interest rate. The numerical analysis shows that, for the specific policy design considered in this paper, a suitable choice of the participation rate combined with the proposed investment strategy minimizes the overall default risk of the insurance company, both in terms of probability of default and expected severit

The purpose of this paper is to analyze the problem of the fair valuation of annuities contracts. The market consistent valuation of these products requires a pricing framework which includes the two main sources of risk affecting the value of the annuity, i.e. interest rate risk and mortality risk. As the IASB has not set any specific guidelines as to which models are the most appropriate for these risks, in this note we consider a range of different models calibrated with historical data. We calculate the fair value of the annuity as a portfolio of zero coupon bonds, each with maturity set equal to the date of the annuity payments; the weights in the portfolio are given by the survival probabilities. Moreover, we focus on the additional information provided by stochastic simulations in order to define a suitable risk margin. The nature of the risk margin is one of the main key issues concerning the IASB and Solvency project.

In this note we introduce a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain deferred annuity pension-type contracts in the UK. The valuation approach is based on the similarity between the payoff structure of the contract and a call option written on a coupon-bearing bond. The model makes use of a one-factor Heath-Jarrow-Morton framework for the term structure of interest rates. Numerical results are investigated and the sensitivity of the price of the option to changes in the\ud key parameters is also analyzed.

In this note, we extend the analysis of the behaviour of the α-quantile option to the case of a contract’s underlying security driven by a Lévy process. To this aim, a simulation procedure based on the order statistics is implemented. The results produced are also used to study the connections between the occurring of a jump in the market and option prices. In particular, we show that, no matter the risk-neutral valuation framework chosen, the occurring of a jump affects the tails of the distribution of the functional which defines the option payoff. Since options pay a premium for the probability mass existing in the tails of such a distribution, this fact might be seen as a first key to interpret the observed biases.

In this communication, we discuss some properties of a class of path dependent options based on the α-quantiles of Brownian motion. In particular we show that such options are well behaved in relation to standard options and comparatively cheaper than an equivalent class of lookback options.

In this paper we propose a simple and effective two-step procedure to estimate the multivariate Lévy model introduced by Ballotta and Bonfiglioli (2012). We assess our estimation approach via simulations, comparing the results with those obtained through a standard but more computationally intensive one-step maximum likelihood estimation. The proposed method is then applied to the computation of the intra-horizon Value at Risk for a portfolio of assets following the model under consideration.

In this paper we apply the multivariate construction for Lévy processes introduced by Ballotta and Bonfiglioli (2014) to propose an integrated model for the joint dynamics of FX exchange rates and asset prices. We show that the proposed construction is consistent in terms of symmetries with respect to inversion and triangulation, and provides an insight into the quanto adjustment showing that this is affected by higher order cumulants of the pure jump part of the systematic risk factor. Using the Esscher transform, we relate Quanto options to vanilla call and put options, which allows for a fast calibration method to the vanilla and the Quanto market. As Quanto products offer significant exposure to the correlation between exchange rates and asset prices, they allow access to a market implied measure of this correlation. By means of a joint calibration exercise to the CME USD denominated Quanto futures on the Nikkei 225 index and both the Nikkei 225 and USDJPY market implied volatilities, we illustrate this approach for the case in which the driving process is assumed to be a Variance Gamma process.

Patients with relapsed/refractory (R/R) peripheral T-cell lymphoma (PTCL) have a poor prognosis, with an expected survival of less than 1 year using standard salvage therapies. Recent advances in our understanding of the biology of PTCL have led to identifying B-Cell Lymphoma 2 (BCL2) protein as a potential therapeutic target. BLC2 inhibitor venetoclax was investigated in a prospective phase II trial in patients with BCL2-positive R/R PTCL after at least one previous standard line of treatment (NCT03552692). Venetoclax given alone at a dosage of 800 mg/day resulted in one complete response (CR) and two stable diseases (SDs) among 17 enrolled patients. The majority of patients (88.2%) interrupted the treatment due to disease progression. No relationship with BCL2 expression was documented. At a median follow-up of 8 months, two patients are currently still on treatment (one CR and one SD). No case of tumor lysis syndrome was registered. Therefore, venetoclax monotherapy shows activity in a minority of patients whose biological characteristics have not yet been identified.Clinical Trial Registrationwww.clinicaltrials.gov (NCT03552692, EudraCT number 2017-004630-29).

Cardiac lymphomas are rare extranodal lymphomas involving primarily and secondarily the heart and/or pericardium. Here we describe three cases of cardiac involvement from lymphoma with specific peculiarities: two primary cardiac Diffuse Large B-cell Lymphomas and one secondary involvement from Marginal Zone Lymphoma (MZL). The first case highlights the issue of early CNS relapse and the possible role for CNS prophylaxis; the second case demonstrates the difficulties of interpretation and possible mistakes of different radiologic techniques adopted to evaluate cardiac involvement by lymphoma during follow-up; the third is a unique case of MZL with cardiac involvement. Our aim is to share the findings observed in these cases putting them in relation with data from the literature.

The occurrence of acute myeloid leukemia (AML) within six months from a diagnosis of breast cancer (BC) is rarely reported in the literature, and it is associated with a poor prognosis. We report herein the case of a 40-year-old woman referred to our centre affected by BC and simultaneous AML. The patient proved refractory to first line therapy and achieved complete remission (CR) with a clofarabine-based regimen followed by allogeneic stem cell transplantation (ASCT). Both during salvage chemotherapy and after ASCT, the patient presented severe infectious complications ( acute cholecistytis and Nocardia pneumonia, respectively) treated with surgery, and currently she is alive in CR for both diseases after 29 months of follow-up. The case highlights the importance of a diagnostic assessment of any unexplained cytopenia in association with solid neoplasia under treatment, underlining the feasibility and priority of a timely treatment of the haematological neoplasm in order to achieve long-term survival.