I study optimal disclosure policies in sequential contests. A contest designer chooses at which periods to publicly disclose the efforts of previous contestants. I provide results for a wide range of possible objectives for the contest designer. While different objectives involve different trade-offs, I that show that under many circumstances the optimal contest is one of the three basic contest structures widely studied in the literature: simultaneous, first-mover, or sequential contest.

We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model combining exact solutions, GBM-type volatility noise, and a stationary volatility density.

This paper presents a framework of developing neural networks for predicting implied volatility surfaces. Conventional financial conditions and empirical evidence related to the implied volatility are incorporated into the neural network architecture design and model training including no static arbitrage, boundaries, asymptotic slope and volatility smile. They are also satisfied empirically by the option data on the S&P 500 index over twenty years. The developed neural network model and its simplified variations outperform the widely used surface stochastic volatility inspired (SSVI) model on the mean average percentage error in both in-sample and out-of-sample datasets. This study has two main methodological contributions. First, an accurate deep learning prediction model is developed and tailored to implied volatility surfaces. Second, a framework, which seamlessly combines data-driven models with financial theories, can be extended and applied to solve other related business problems.

The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz [2001] is widely used for pricing American options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of removing it necessitates doubling simulations. We present the leave-one-out LSM (LOOLSM) algorithm for efficiently eliminating look-ahead bias. We validate the method with several option examples, including the multi-asset cases that the LSM algorithm significantly overvalues. We also obtain the convergence rates of look-ahead bias by measuring it using the LOOLSM method. The analysis and computational evidence support our findings.

We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a utility maximization problem under hyperbolic absolute risk aversion (HARA) risk preferences. By analyzing the associated Hamilton-Jacobi-Bellman equation, we derive the exact conditions under which the equation admits a solution and solve the utility maximization explicitly. A series of numerical examples are provided to illustrate the optimal strategies and examine the effects of model parameters.

Despite the success of demand response programs in retail electricity markets in reducing average consumption, the random responsiveness of consumers to price event makes their efficiency questionable to achieve the flexibility needed for electric systems with a large share of renewable energy. The variance of consumers' responses depreciates the value of these mechanisms and makes them weakly reliable. This paper aims at designing demand response contracts which allow to act on both the average consumption and its variance. The interaction between a risk--averse producer and a risk--averse consumer is modelled through a Principal--Agent problem, thus accounting for the moral hazard underlying demand response contracts. We provide closed--form solution for the optimal contract in the case of constant marginal costs of energy and volatility for the producer and constant marginal value of energy for the consumer. We show that the optimal contract has a rebate form where the initial condition of the consumption serves as a baseline. Further, the consumer cannot manipulate the baseline at his own advantage. The second--best price for energy and volatility are non--constant and non--increasing in time. The price for energy is lower (resp. higher) than the marginal cost of energy during peak--load (resp. off--peak) periods. We illustrate the potential benefit issued from the implementation of an incentive mechanism on the responsiveness of the consumer by calibrating our model with publicly available data. We predict a significant increase of responsiveness under our optimal contract and a significant increase of the producer satisfaction.

Retirement gratuity is the money companies typically pay their employees at the end of their contracts or at the time of leaving the company. It is a defined benefit plan and is often given as an alternative to a pension plan. In Botswana, there is now a new pattern whereby companies give their employees the option to receive their gratuity at various stages before the end of their contracts. In particular, some companies give their employees an option to receive their gratuity on a monthly basis rather than having them wait for a year or more. Many employees find this option attractive, but is it economically sound? This paper sheds light on this question by quantifying the economic benefits of the tax relief provided by government relative to investing the monthly-received funds in a risk-free savings account or helping repay a loan. The principles and methods used herein can be adapted and applied to different taxation systems.

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\'epey (2015a) and Cr\'epey (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.

We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key properties related to hitting time probabilities via the simulation.

Motivated by the evidence that real-world networks evolve in time and may exhibit non-stationary features, we propose an extension of the Exponential Random Graph Models (ERGMs) accommodating the time variation of network parameters. Within the ERGM framework, a network realization is sampled from a static probability distribution defined parametrically in terms of network statistics. Inspired by the fast growing literature on Dynamic Conditional Score-driven models, in our approach, each parameter evolves according to an updating rule driven by the score of the conditional distribution. We demonstrate the flexibility of the score-driven ERGMs, both as data generating processes and as filters, and we prove the advantages of the dynamic version with respect to the static one. Our method captures dynamical network dependencies, that emerge from the data, and allows for a test discriminating between static or time-varying parameters. Finally, we corroborate our findings with the application to networks from real financial and political systems exhibiting non stationary dynamics.