COMMERCIAL AND INDUSTRIAL MATHEMATICS

Carol Alexander, University of Sussex (presentation)
Nice Moment Swaps

This talk presents the very latest research on moment swaps, starting with a simple new definition of realised variance that yields discretely monitored variance swaps with none of the usual pricing errors (viz. from jumps and from the use of an integral rather than a sum in the derivation of fair value). We then generalize the set of moment characteristics which satisfy Neuberger’s aggregation property and explain how the fair values of such moment swaps may be obtained by pricing some fundamental contacts (e.g. the log and entropy contracts) based on vanilla option prices. Our methodology relies solely on the assumption of an arbitrage-free market and is therefore relevant for a wide range of applications.
(Jointly with Johannes Rauch).

Sergey Nadtochiy, University of Michigan (presentation)
Weak Reflection Principle and Static Hedging of Barrier Options

The classical Reflection Principle is a technique that allows one to express the joint distributionof a Brownian motion and its running maximum through the distribution of the process itself. It relies on the specific symmetry and continuity properties of a Brownian motion and, therefore, cannot be directly applied to an arbitrary Markov process. We show that, in fact, there exists a weak formulation of this method that allows us to recover the same results on the joint distribution of a Brownian motion and its running maximum. We call this method a Weak Reflection Principle and show that it can be extended to a large class of Markov processes, which do not posses any symmetry properties and are allowed to have jumps. We demonstrate various applications of this technique in Finance, Computational Methods, Physics, and Biology. In particular, we show that theWeak Reflection Principle provides an exact solution to the problem of hedging Barrier options with a semi-static position in European type claims. Our method allows us to find such hedging strategies in the diffusion- and L´evy-based models. In addition, we show how it can be used to establish robust static hedging strategies that are model-independent. We illustratethe theory with numerical examples.

Albert S. (Pete) Kyle, University of Maryland (presentation) (video archive of talk)
Market Microstructure Invariance: Theory and Empirical Tests

Using the intuition that financial markets transfer risks in business time, we define “market microstructure invariance” as the hypothesis that the size distribution of risk transfers (“bets”) and transaction costs of their implementation are constant across assets and time. A meta-model suggests that microstructure invariance is ultimately related to granularity of information flow. Based on a database of 400,000+ portfolio transition trades, we show that quantitative predictions of microstructure invariance concerning bets sizes and transaction costs as functions of observable volume and volatility closely match the data. We calibrate invariants and discuss implications for financial markets.

Andreea Minca, Cornell University *Talk Cancelled
When Do Creditors with Heterogeneous Beliefs Agree to Run?

We explore, in a multi-period setting, the funding liquidity of a borrower that finances its operations through short term debt. The short term debt is provided by a continuum of agents with heterogeneous beliefs about the prospects of the borrower. In each period, creditors observe the borrower’s fundamentals and decide on the amount they invest in its short term debt. We formalize this problem as a coordination game, and we show that there exists a unique reasonable Nash equilibrium. We show that the borrower is able to refinance if and only if the liquid net worth is above an illiquidity barrier, and we explicitly find this barrier in terms of the distribution of capital and beliefs across agents.
(joint with Andrey Krishenik and Johannes Wissel).

That in financial crises, central banks should become lenders of last resort to the economy, while taking into account fi nancial risk management and moral hazard concerns, is well known ever since the 19th century experience of the Bank of England as documented in Bagehot (1873) or King (1936). In this paper, we develop further the relevant trade-o ffs. First, we argue that the credit riskiness of counterparties and issuers is endogenous to central bank's financial crisis measures and the related risk control framework. It is shown that ignoring this can lead to sub-optimal risk management decisions. Second, extending the problem of the central bank from a pure risk management perspective to one considering economic efficiency, the central bank also needs to consider how to avoid to the extent possible (a) defaults of viable but illiquid institutions, and (b) the preservation through central bank lending of loss-making and non-viable institutions. Finally, we formalize these ideas by providing a stylized model capturing the effects of central bank collateral haircuts on both central bank risk-taking and economic efficiency. The model illustrates that (i) central bank risk-taking can decrease or increase when haircuts are increased; (ii) economic efficiency and central bank risk-taking are in many cases non-monotonous functions of haircuts on collateral; (iii) that, as expected, central bank risk-taking and economic efficiency are not necessarily aligned. The model explains why in a financial crisis, in which liquidity shocks become more erratic and the social costs of defaults increase, central banks tend to make the collateral framework less restrictive (CGFS, 2008).
Central bank liquidity provision, risk-taking and economic efficiency

Mike Lipkin (Katama Trading and Columbia University) (presentation)
Market turbulence, monetization, and universality.

Shocks in financial markets create regions of turbulence which are out-of-equilibrium. Prices in this region are frequently monetizable. Are there universal properties? Some of the work presented here was done by Columbia University students in the course Experimental Finance.

Julien Guyon, Bloomberg (presentation) (video archive of the talk)
Stochastic Volatility's Orderly Smiles

We consider multi-factor stochastic volatility models and derive the volatility smile at order two in the volatility-of-volatility. At this order, the smile is quadratic in log-moneyness and depends on three effective quantities within which the dynamics of the spot and forward variances of any particular model is condensed. We supply explicit expressionsof these quantities for a family of Heston-like models as well as a 2-factor version of the Bergomi model. For this model, comparison with the exact smiles shows good agreement for volatility-of-volatility levels that are typical ofequity underlyings. Finally we derive short term asymptotics and highlight the structural dependence of the level of ATM skew and curvature on the ATM volatility, and we link the decay of ATM skew and curvature for long maturities to the time decay of spot/variance and variance/variance covariance functions.

Jon Gregory, Solum Financial Partners (presentation) (video archive of the talk)
Why CDOs Work

Prior to the beginning of the global financial crisis in 2007, the CDO was a successful financial innovation. However, CDOs have been blamed for causing the crisis, pricing models for CDOs have been heavily criticised, litigation has been rife and investor demand has almost disappeared. All players in the CDO market, notably banks, rating agencies as well as investors have suffered as a result. An obvious question to ask is whether the concept of a CDO is flawed and the market was doomed to eventual failure or if CDOs, like many other financial investments, were simply a casualty of a largely unforeseen and completely unprecedented global financial crisis. In this talk, I provide an answer to this question based on empirical analysis of corporate default rates and a typical CDO structure.

 

Paul Ormerod (Volterra Partners LLP) (presentation) (video archive of the talk)
Trying to Make Economics a Science: Key Empirical Features of Recessions and Thoughts on How to Explain Them

The current financial crisis has attracted a huge amount of attention. But economic recessions are not new. There have been over 200 individual examples across the individual Western countries since the late 19th century. Mainstream economic models, with their focus on equilibrium, are quite unable to explain the key empirical features such as distribution of duration and size. How might we go about building models which do? Feedback is essential, and agent based models also allow diversity of behaviour. These seem promising ways of moving forward.

Nov. 23

Peter Carr (Morgan Stanley) (presentation) (video archive of the talk)
Risk, Return and Ross Recovery

The risk return relation is a staple of modern finance. When risk is measured by volatility, it is well known that option prices convey risk. One of the more influential ideas in the last twenty years is that the conditional volatility of an asset price can also be inferred from the market prices of options written on that asset. Under a Markovian restriction, it follows that risk-neutral transition probabilities can also be determined from option prices. Recently, Ross has shown that real-world transition probabilities of a Markovian state variable can be recovered from its risk-neutral transition probabilities along with a restriction on preferences. In recent work with Jiming Yu, we show how to recover real-world transition probabilities in a bounded diffusion context in a preference-free manner. Our approach is instead based on restricting the form and dynamics of the numeraire portfolio.

Paul Kaplan ( Morningstar) (presentation) (video archive of the talk)
Alpha, Beta, and Now... Gamma

When it comes to generating retirement income, investors arguably spend the most time and effort on selecting 'good' investment funds/managers-the so called alpha decision-as well as the asset allocation, or beta, decision. However, alpha and beta are just two elements of a myriad of important financial planning decisions, many of which can have a far more significant impact on retirement income. We introduce a new concept called "Gamma" designed to quantify the additional expected retirement income achieved by an individual investor from making more intelligent financial planning decisions. Gamma will vary for different types of investors, but in this article we focus on five fundamental financial planning decisions/techniques: a total wealth framework to determine the optimal asset allocation, a dynamic withdrawal strategy, incorporating guaranteed income products (i.e., annuities), tax-efficient decisions, and liability-relative asset allocation optimization. We estimate a retiree can expect to generate 29% more income on a "utility-adjusted" basis using a Gamma-efficient retirement income strategy when compared to our base scenario, which assumes a 4% constant real withdrawal and a 20% equity allocation portfolio. This additional income is equiva- lent to an annual arithmetic return increase of +1.82% (i.e., Gamma equivalent alpha), which represents a significant improvement in portfolio efficiency for a retiree. Unlike traditional alpha, which can be hard to predict, we find that Gamma (and Gamma equivalent alpha) can be achieved by anyone following an efficient financial planning strategy.


***This month's seminar will host one speaker and end at 6:30 p.m.

Yacine Ait-Sahalia (Princeton University) (presentation) (video archive of the talk)
The Term Structure of Variance Swaps, Risk Premia and the Expectation Hypothesis

We study the term structure of variance swaps, which are popular volatility derivative contracts. A model-free analysis reveals a significant jump risk component embedded in variance swaps. The variance risk premium is negative and has a downward sloping term structure. Variance risk premia due to negative jumps present similar features in quiet times but have an upward sloping term structure in turbulent times. This suggests that short-term variance risk premia mainly reflect investors' fear of a market crash. Theoretically, the Expectation Hypothesis does not hold, but biases and inefficiencies are modest for short time horizons. A simple trading strategy with variance swaps generates significant returns.
This is a joint work with Mustafa Karaman and Loriano Mancini.

Carole Bernard (University of Waterloo) (presentation) (video archive of the talk)
Mean-Variance Optimal Portfolios in the Presence of a Benchmark and Application to Fraud Detection

We first study mean-variance efficient portfolios when there are no trading constraints. Optimal strategies amount to holding a short position in the stochastic discount factor used for pricing. We show that optimal strategies perform poorly in bear markets. We then depart from the traditional setting and assume investors use a stochastic benchmark (linked to the market) as a reference portfolio. Preferences become state-dependent and we are able to accomodate for this. Precisely, we derive mean-variance efficient portfolios when investors aim to achieve a given correlation (or a given dependence structure) with a stochastic benchmark. We also provide bounds on Sharpe ratios and show how these can be useful for fraud detection. For example it is shown that under some conditions it is not possible for investment funds
to display negative correlation with the financial market and to have a positive Sharpe ratio.