Pricing and hedging of credit derivatives via?the?innovations approach to nonlinear filtering

In this paper, we propose a new, information-based approach for modelling the dynamic evolution of a portfolio of credit risky securities. In our setup, market prices of traded credit derivatives are given by the solution of a nonlinear filtering problem. The innovations approach to nonlinear filtering is used to solve this problem and to derive the dynamics of market prices. Moreover, the practical application of the model is discussed: we analyse calibration, the pricing of exotic credit derivatives and the computation of risk-minimizing hedging strategies. The paper closes with a few numerical case studies.     

Exchange rate dynamics under state-contingent stochastic process switching

This paper offers a closed-form solution of a process switching problem, i.e., switching the exchange rate regime from free-floating to a completely fixed one. An example of such regime change is the adoption of the Euro. In contrast to previous studies on the subject, this paper analyzes a specific case when foreign exchange market participants consider both the Euro locking rate and locking date as uncertain. Preceding the locking, the exchange rate is determined by three factors: fundamental, market expectations for the Euro locking rate, and date. The model is used to examine the conditions under which the exchange rate volatility is mitigated by the prospect of locking.     

Optimal order placement in limit order markets

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by characteristics of the order flows and queue sizes in each limit order book, as well as the structure of transaction fees and rebates across exchanges. We propose a quantitative framework for studying this order placement problem by formulating it as a convex optimization problem. This formulation allows the study of how the optimal order placement decision depends on the interplay between the state of order books, the fee structure, order flow properties and the aversion to execution risk. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general case of order placement across multiple exchanges, we propose a stochastic algorithm that computes the optimal routing policy and study the sensitivity of the solution to various parameters. Our algorithm does not require an explicit statistical model of order flow but exploits data on recent order fills across exchanges in the numerical implementation of the algorithm to acquire this information through a supervised learning procedure.     

Portfolio optimization under model uncertainty and BSDE games

We consider robust optimal portfolio problems for markets modeled by (possibly non-Markovian) Itô–Lévy processes. Mathematically, the situation can be described as a stochastic differential game, where one of the players (the agent) is trying to find the portfolio that maximizes the utility of her terminal wealth, while the other player (“the market”) is controlling some of the unknown parameters of the market (e.g., the underlying probability measure, representing a model uncertainty problem) and is trying to minimize this maximal utility of the agent. This leads to a worst case scenario control problem for the agent. In the Markovian case, such problems can be studied using the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation, but these methods do not work in the non-Markovian case. We approach the problem by transforming it into a stochastic differential game for backward stochastic differential equations (a BSDE game). Using comparison theorems for BSDEs with jumps we arrive at criteria for the solution of such games in the form of a kind of non-Markovian analogue of the HJBI equation. The results are illustrated by examples.     

Designing proxies for stock market indices is computationally hard*

In this paper, we study the problem of designing proxies (or portfolios) for various stock market indices based on historical data. We use four different methods for computing market indices, all of which are formulae used in actual stock market analysis. For each index, we consider three criteria for designing the proxy: the proxy must either track the market index, outperform the market index, or perform within a margin of error of the index while maintaining a low volatility. In eleven of the twelve cases (all combinations of four indices with three criteria except the problem of sacrificing return for less volatility using the price-relative index) we show that the problem is NP-hard, and hence most likely intractable.     

Optimal portfolio delegation when parties have different coefficients of risk aversion

We consider the problem of delegated portfolio management when the involved parties are risk-averse. The agent invests the principal's money in the financial market, and in return he receives a compensation which depends on the value that he generates over some period of time. We use a dual approach to explicitly solve the agent's problem analytically and subsequently we use this solution to solve the principal's problem numerically. The interaction between the principal's and the agent's risk aversion and the optimal compensation scheme is studied and, for example, in the case of the more risk averse agent according to common folklore the principal should optimally choose a fee schedule such that the agent's derived risk aversion decreases. We illustrate that this is not always the case.     

Personal Taxation in Firm Market Valuation: Theory and Test*

In this paper, I extend Ohlson's 1995 firm market valuation model to incorporate personal taxes: the taxes on dividends and the taxes on capital gains. Without personal taxes, firm market value can be expressed as the present value of future benefits received by the shareholders (dividends, in this case). With personal taxes, the benefits received by the shareholders should be classified into three categories (due to their different tax treatments): dividends, share repurchases, and new share issues (i.e., contributed capital). The extended model shows the effects of personal taxation on firm market valuation: retained earnings are valued less than contributed stocks, both dividends taxes and capital gains taxes affect retained earnings valuation and firm market value, and firms choose cash distribution methods (paying dividends and repurchasing shares) to increase their retained earnings valuation, therefore increasing their market value. An empirical test using a sample from the Disclosure Select Canada and Financial Post Card data bases for the years 1995‐98 supports these personal tax effects.