In a simplified setting, we show how to price invoice non-recourse factoring taking into account not only the credit worthiness of the debtor but also the assignor's one, together with the default correlation between the two. Indeed, the possible default of the assignor might impact the payoff by means of the bankruptcy revocatory, especially in case of undisclosed factoring.

A new procedure is presented for the objective comparison and evaluation of default definitions. This allows the lender to find a default threshold at which the financial loss of a loan portfolio is minimised, in accordance with Basel II. Alternative delinquency measures, other than simply measuring payments in arrears, can also be evaluated using this optimisation procedure. Furthermore, a simulation study is performed in testing the procedure from `first principles' across a wide range of credit risk scenarios. Specifically, three probabilistic techniques are used to generate cash flows, while the parameters of each are varied, as part of the simulation study. The results show that loss minima can exist for a select range of credit risk profiles, which suggests that the loss optimisation of default thresholds can become a viable practice. The default decision is therefore framed anew as an optimisation problem in choosing a default threshold that is neither too early nor too late in loan life. These results also challenges current practices wherein default is pragmatically defined as `90 days past due', with little objective evidence for its overall suitability or financial impact, at least beyond flawed roll rate analyses or a regulator's decree.

In this article, we tackle the problem of a market maker in charge of a book of equity derivatives on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an equity option market maker is in fact tractable. More precisely, the problem faced by an equity option market maker is characterized by a two-dimensional functional equation that can be solved numerically using interpolation techniques and classical Euler schemes, even for large portfolios. Numerical examples are provided for a large book of equity options.

In this work we want to provide a general principle to evaluate the CVA (Credit Value Adjustment) for a vulnerable option, that is an option subject to some default event, concerning the solvability of the issuer. CVA is needed to evaluate correctly the contract and it is particularly important in presence of WWR (Wrong Way Risk), when a credit deterioration determines an increase of the claim's price. In particular, we are interested in evaluating the CVA in stochastic volatility models for the underlying's price (which often fit quite well the market's prices) when admitting correlation with the default event. By cunningly using Ito's calculus, we provide a general representation formula applicable to some popular models such as SABR, Hull \& White and Heston, which explicitly shows the correction in CVA due to the processes correlation. Later, we specialize this formula and construct its approximation for the three selected models. Lastly, we run a numerical study to test the formula's accuracy, comparing our results with Monte Carlo simulations.

Subordination is an often used stochastic process in modeling asset prices. Subordinated Levy price processes and local volatility price processes are now the main tools in modern dynamic asset pricing theory. In this paper, we introduce the theory of multiple internally embedded financial time-clocks motivated by behavioral finance. To be consistent with dynamic asset pricing theory and option pricing, as suggested by behavioral finance, the investors' view is considered by introducing an intrinsic time process which we refer to as a behavioral subordinator. The process is subordinated to the Brownian motion process in the well-known log-normal model, resulting in a new log-price process. The number of embedded subordinations results in a new parameter that must be estimated and this parameter is as important as the mean and variance of asset returns. We describe new distributions, demonstrating how they can be applied to modeling the tail behavior of stock market returns. We apply the proposed models to modeling S&P 500 returns, treating the CBOE Volatility Index as intrinsic time change and the CBOE Volatility-of-Volatility Index as the volatility subordinator. We find that these volatility indexes are not proper time-change subordinators in modeling the returns of the S&P 500.

We introduce and study the notion of sure profit via flash strategy, consisting of a high-frequency limit of buy-and-hold trading strategies. In a fully general setting, without imposing any semimartingale restriction, we prove that there are no sure profits via flash strategies if and only if asset prices do not exhibit predictable jumps. This result relies on the general theory of processes and provides the most general formulation of the well-known fact that, in an arbitrage-free financial market, asset prices (including dividends) should not exhibit jumps of a predictable direction or magnitude at predictable times. We furthermore show that any price process is always right-continuous in the absence of sure profits. Our results are robust under small transaction costs and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.

We propose a continuous-time model of trading with heterogeneous beliefs. Risk-neutral agents face quadratic costs-of-carry on positions and thus their marginal valuations decrease with the size of their position, as it would be the case for risk-averse agents. In the equilibrium models of heterogeneous beliefs that followed Harrison-Kreps, investors are risk-neutral, short-selling is prohibited and agents face constant marginal costs of carrying positions. The resulting resale option guarantees that the price exceeds the price of the asset when speculation is ruled out; the difference is identified as a bubble. In our model increasing marginal costs entail that the price depends on asset supply. Second, agents also value an option to delay, and this may cause the market to equilibrate below the buy-and-hold price. Third, we introduce the possibility of short-selling. A Hamilton-Jacobi-Bellman equation of a novel form quantifies precisely the influence of the costs-of-carry on the price. An unexpected decrease in shorting costs may lead to the collapse of a bubble; this links the financial innovations that facilitated shorting of MBSs to the subsequent collapse of prices.

This article analyzes the role of Finnish regulation in achieving the broadband penetration goals defined by the National Regulatory Authority. It is well known that in the absence of regulatory mitigation the population density has a positive effect on broadband diffusion. Hence, we measure the effect of the population density on the determinants of broadband diffusion throughout the postal codes of Finland via Geographically Weighted Regression. We suggest that the main determinants of broadband diffusion and the population density follow a spatial pattern that is either concentric with a weak/medium/strong strength or non-concentric convex/concave. Based on 10 patterns, we argue that the Finnish spectrum policy encouraged Mobile Network Operators to satisfy ambitious Universal Service Obligations without the need for a Universal Service Fund. Spectrum auctions facilitated infrastructure-based competition via equitable spectrum allocation and coverage obligation delivery via low-fee licenses. However, state subsidies for fiber deployment did not attract investment from nationwide operators due to mobile preference. These subsidies encouraged demand-driven investment, leading to the emergence of fiber consumer cooperatives. To explain this emergence, we show that when population density decreases, the level of mobile service quality decreases and community commitment increases. Hence, we recommend regulators implementing market-driven strategies for 5G to stimulate local investment. For example, by allocating the 3.5 GHz and higher bands partly through local light licensing.