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## Financial stability and Basel II

### Annals of Finance (2007-01-01) 3: 107-130 , January 01, 2007

The Basel II Advanced Internal Ratings (AIRB) approach is compared to capital requirements set using an equilibrium structural credit risk model. Analysis shows the AIRB approach undercapitalizes credit risk relative to regulatory targets and allows wide variation in capital requirements for a given exposure owing to ambiguity in the definitions of loss given default and exposure at default. In contrast, the Foundation Internal Ratings Based (FIRB) approach may over-capitalize credit risk relative to supervisory objectives. It is unclear how Basel II will buttress financial sector stability as it specifies the weakest regulatory capital standard for large complex AIRB banks.

## On the necessity of five risk measures

### Annals of Finance (2012-11-01) 8: 533-552 , November 01, 2012

The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an important role in computing the capital for both approaches. In this paper we analyze the errors produced by using this measure. We discuss other measures, demonstrating their strengths and shortcomings. We give examples, showing the need for the information from multiple risk measures in order to determine a bank’s loss distribution. We conclude by suggesting a regulatory requirement of multiple risk measures being reported by banks, giving specific recommendations.

## Bounds for path-dependent options

### Annals of Finance (2015-11-01) 11: 433-451 , November 01, 2015

We develop new semiparametric bounds on the expected payoffs and prices of European call options and a wide range of path-dependent contingent claims. We first focus on the trinomial financial market model in which, as is well-known, an exact calculation of derivative prices based on no-arbitrage arguments is impossible. We show that the expected payoff of a European call option in the trinomial model with martingale-difference log-returns is bounded from above by the expected payoff of a call option written on an asset with i.i.d. symmetric two-valued log-returns. We further show that the expected payoff of a European call option in the multiperiod trinomial option pricing model is bounded by the expected payoff of a call option in the two-period model with a log-normal asset price. We also obtain bounds on the possible prices of call options in the (incomplete) trinomial model in terms of the parameters of the asset’s distribution. Similar bounds also hold for many other contingent claims in the trinomial option pricing model, including those with an arbitrary convex increasing payoff function as well as for path-dependent ones such as Asian options. We further obtain a wide range of new semiparametric moment bounds on the expected payoffs and prices of path-dependent Asian options with an arbitrary distribution of the underlying asset’s price. These results are based on recently obtained sharp moment inequalities for sums of multilinear forms and *U*-statistics and provide their first financial and economic applications in the literature. Similar bounds also hold for many other path-dependent contingent claims.

## Pricing and managing risks of European-style options in a Markovian regime-switching binomial model

### Annals of Finance (2013-08-01) 9: 421-438 , August 01, 2013

We discuss the pricing and risk management problems of standard European-style options in a Markovian regime-switching binomial model. Due to the presence of an additional source of uncertainty described by a Markov chain, the market is incomplete, so the no-arbitrage condition is not sufficient to fix a unique pricing kernel, hence, a unique option price. Using the minimal entropy martingale measure, we determine a pricing kernel. We examine numerically the performance of a simple hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as Value at Risk and Expected Shortfall. The impacts of the frequency of re-balancing the hedging portfolio and the transition probabilities of the modulating Markov chain on the quality of hedging are also discussed.

## Gaussian and logistic adaptations of smoothed safety first

### Annals of Finance (2014-05-01) 10: 333-345 , May 01, 2014

In one model of portfolio choice, dating to the Safety First principle, the investor is assumed to select assets to minimize the probability of realizing a portfolio return below some pre-determined target or benchmark rate of return. This paper builds on a recent refinement of Safety First—Smoothed Safety First—but is distinct in that it uses Gaussian and logistic distributions instead of the extreme value type-I distribution. Empirical and simulation results suggest that these alternative smoothing functions perform very much like the original formulation, suggesting that smoothing is robust to the choice of smoothing function for suitably large samples. For smaller samples, both Smoothed Safety First and the standard normal-based smoothing function appear to deliver portfolios with slightly smaller shortfall probabilities than the logistic-based approach.

## Intragroup transfers, intragroup diversification and their risk assessment

### Annals of Finance (2016-12-01) 12: 363-392 , December 01, 2016

When assessing group solvency, an important question is to what extent intragroup transfers may be taken into account, as this determines to which extent diversification can be achieved. We suggest a framework to explicitly describe the families of admissible transfers that range from the free movement of capital to excluding any transactions. The constraints on admissible transactions are described as random closed sets. The paper focuses on the corresponding solvency tests that amount to the existence of acceptable selections of the random sets of admissible transactions.

## Common Shocks and Relative Compensation

### Annals of Finance (2006-10-01) 2: 407-420 , October 01, 2006

This paper studies qualitative properties of an optimal contract in a multi-agent setting in which agents are subject to a common shock. We derive a necessary and sufficient condition for the optimal reward of an agent producing an output level *y* to be a decreasing (increasing) function of the outputs of the other agents, under the assumption that the agents’ outputs are informative signals of the value of the common shock. The condition is that the likelihood ratio *p*(*y*, *e*, *η*)/*p*(*y*, *e*′, *η*), where *e* is a higher effort level than *e*′ and *η* is the value of the common shock, be a decreasing (increasing) function of *η*. We give examples of applications of the result and examine its consequences for CEO compensation.

## Quadratic minimization with portfolio and intertemporal wealth constraints

### Annals of Finance (2017-08-01) 13: 299-340 , August 01, 2017

We address a problem of stochastic optimal control motivated by portfolio optimization in mathematical finance, the goal of which is to minimize the expected value of a general quadratic loss function of the wealth at close of trade when there is a specified convex constraint on the portfolio, together with a specified almost-sure lower-bound on intertemporal wealth over *the full trading interval*. A precursor to the present work, by Heunis (Ann Financ 11:243–282, 2015), addressed the simpler problem of minimizing a general quadratic loss function with a convex portfolio constraint and a stipulated almost-sure lower-bound on the wealth only *at close of trade*. In the parlance of optimal control the problem that we shall address here exhibits the combination of a *control constraint* (i.e. the portfolio constraint) together with an almost-sure *intertemporal state constraint* (on the wealth over the full trading interval). Optimal control problems with this combination of constraints are well known to be quite challenging even in the deterministic case, and of course become still more so when one deals with these same constraints in a stochastic setting. We nevertheless find that an ingenious variational approach of Rockafellar (Conjugate duality and optimization, CBMS-NSF series no. 16, SIAM, 1974), which played a key role in the precursor work noted above, is fully equal to the challenges posed by this problem, and leads naturally to an appropriate vector space of *dual variables*, together with a *dual functional* on the space of dual variables, such that the *dual problem* of maximizing the dual functional is guaranteed to have a solution (or Lagrange multiplier) when the problem constraints satisfy a simple and natural *Slater condition*. We then establish *necessary and sufficient* conditions for the optimality of a candidate wealth process in terms of the Lagrange multiplier, and use these conditions to construct an optimal portfolio.

## On the positive fundamental value of money with short-sale constraints

### Annals of Finance (2007-10-01) 3: 455-469 , October 01, 2007

This paper is concerned with the pricing of money in a framework with restrictions on trading, under an extension of the standard-asset pricing theory that recognizes both tangible and intangible returns. It is argued that the underlying motivations for demanding money give content to its fundamental value and the bubble component. This approach is illustrated by analyzing the case where no short-sales are allowed, as two examples from the literature are made used to assert that money is a pure pricing bubble. Owing to this setup exhibits technically incomplete financial markets, the fundamental value of money is not uniquely defined over the set of generalized state-price processes. Then, these examples are shown to comprise an extreme case, as money is a pure store of value for the state-prices chosen (i.e., it is a pricing bubble). Instead, the fundamental value of money can be positive for other state-prices, representing the role of money in the trading process. Therefore, money should not be considered the equivalent of a pure pricing bubble.

## Banking competition and welfare

### Annals of Finance (2017-02-01) 13: 31-53 , February 01, 2017

We develop a simple general equilibrium model in which investment in a risky technology is subject to moral hazard and banks can extract market power rents. We show that more bank competition results in lower economy-wide risk, higher social welfare, lower bank capital ratios, more efficient production plans and Pareto-ranked real allocations. Perfect competition supports a second best allocation and optimal levels of bank risk and capitalization. These results are at variance with those obtained by a large literature that has studied a similar environment in partial equilibrium, they are empirically relevant, and carry significant implications for policy guidance.