Related papers: Black to Negative: Embedded optionalities in commo…
In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries…
When imperfect quality products are produced in a production process, rework may be performed to make them become serviceable. In an inventory system, items may deteriorate. Selling deteriorated items to customers will create negative…
We introduce pricing formulas for competition and collusion models of two-sided markets with an outside option. For the competition model, we find conditions under which prices and consumer surplus may increase or decrease if the outside…
In financial mathematics, it is a typical approach to approximate financial markets operating in discrete time by continuous-time models such as the Black Scholes model. Fitting this model gives rise to difficulties due to the discrete…
This paper presents a convenient framework for modeling default process and pricing derivative securities involving credit risk. The framework provides an integrated view of credit valuation adjustment by linking distance-to-default,…
The short maturity limit $T\to 0$ for the implied volatility of an Asian option in the Black-Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note we derive the…
Catastrophe risk is a major threat faced by individuals, companies, and entire economies. Catastrophe (CAT) bonds have emerged as a method to offset this risk and a corresponding literature has developed that attempts to provide a…
Accountability is an often called for property of technical systems. It is a requirement for algorithmic decision systems, autonomous cyber-physical systems, and for software systems in general. As a concept, accountability goes back to the…
In calculi for modelling communication protocols, internal and external choices play dual roles. Two external choices can be viewed naturally as dual too, as they represent an agreement between the communicating parties. If the interaction…
Considering cylindrical topology we present the static solution for a charged black hole in conformal gravity. We show that unlike the general relativistic case there are two different solutions, both including a factor that when set to…
We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical…
The writers propose a mathematical Method for deriving risk weights which describe how a borrower's income, relative to their debt service obligations (serviceability) affects the probability of default of the loan. The Method considers the…
A central push in operations models over the last decade has been the incorporation of models of customer choice. Real world implementations of many of these models face the formidable stumbling block of simply identifying the `right' model…
In the last years many accurate decision support systems have been constructed as black boxes, that is as systems that hide their internal logic to the user. This lack of explanation constitutes both a practical and an ethical issue. The…
In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the…
Suppliers (including companies and individual prosumers) may wish to protect their private information when selling items they have in stock. A market is envisaged where private information can be protected through the use of differential…
This work studies the valuation of currency options in markets suffering from a financial crisis. We consider a European option where the underlying asset is a foreign currency. We assume that the value of the underlying asset is a…
In this paper, we study the asymptotic behavior of Asian option prices in the worst case scenario under an uncertain volatility model. We give a procedure to approximate the Asian option prices with a small volatility interval. By imposing…
Valuation and parity formulas for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, possibility of default and "bubbles" in asset prices. The formulas are given via…
Existing approaches to asset-pricing under model-uncertainty adapt classical utility-maximization frameworks and seek theoretical comprehensiveness. We move toward practice by considering binary model-risks and by emphasizing 'constraints'…