2012 / 2013

Title: Asymptotics for Exponential Lévy Processes and their Volatility Smile: Survey and New Results

Abstract: 

Exponential Lévy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes, and the corresponding implied volatility surfaces have been analyzed in some detail. In the non-asymptotic regimes, option prices are described by the Lewis-Lipton formula which allows one to represent them as Fourier integrals; the prices can be trivially expressed in terms of their implied volatility. Recently, attempts at calculating the asymptotic limits of the implied volatility have yielded several expressions for the short-time, long-time, and wing asymptotics. In order to study the volatility surface in required detail, in this paper we use the FX conventions and describe the implied volatility as a function of the Black-Scholes delta. Surprisingly, this convention is closely related to the resolution of singularities frequently used in algebraic geometry. In this framework, we survey the literature, reformulate some known facts regarding the asymptotic behaviour of the implied volatility, and present several new results. We emphasize the role of fractional differentiation in studying the tempered stable exponential Lévy processes and derive novel numerical methods based on judicial finite-difference approximations for fractional derivatives. We also briefly demonstrate how to extend our results in order to study important cases of local and stochastic volatility models, whose close relation to the Lévy process based models is particularly clear when the Lewis-Lipton formula is used. Our main conclusion is that studying asymptotic properties of the implied volatility, while theoretically exciting, is not always practically useful because the domain of validity of many asymptotic expressions is small.

Date: Tuesday 9th October, 17:00 - 18:00

Event Location: Lecture Theatre, Trinity Hall

Title: Bankruptcy and Delinquency in a Model of Unsecured Debt 

Abstract:

Limited commitment for the repayment of consumer debt comes from two places:

formal laws granting a partial or complete discharge for debts under certain circumstances, or “bankruptcy,” and informal default and renegotiation, or “delinquency.” In the US, both channels are used routinely. The usefulness of each of these routes as a way out of debt depends on the costs and benefits available through the other: delinquency exposes a household to collections processes initiated by lenders, while formal bankruptcy appears to carry more visible consequences for future transactions, including restrictions to even secured forms of credit. This paper is the first, to our knowledge, to evaluate unsecured consumer credit markets in the presence of both bankruptcy and delinquency. We show that these two options indeed interact in important ways. Specifically, we show that stricter control of delinquency, as defined by a relatively high ability to garnish wages, leads to more bankruptcy and lower welfare. Similarly, we find that eliminating the bankruptcy option altogether leads to a modest increase in delinquency. Perhaps most interestingly, we show that interest-rate ceilings, even though they have the standard effects in terms of limiting credit access, improve ex-ante welfare for all. This occurs because the inability to reprice debt after delinquency allows a useful level of “state contingency” in debt that does not increase average borrowing costs substantially. In essence, households have to pay the costs of delinquency in order to get the benefits of a low interest rate.

Date: Tuesday 23rd October, 17:00 - 18:00

Event Location: Sidgwick Hall, Newnham College

Title: Quantitative easing in the UK: evidence from financial markets on QE1 and QE2

Abstract:

During the recent financial crisis the Bank of England, like many other central banks, loosened monetary policy using both conventional and unconventional measures.  The main unconventional measure used by the Bank was the policy of asset purchases – mainly of government bonds - financed by the creation of central bank money, so-called quantitative easing (QE).  During March 2009 to January 2010 and October 2011 to May 2012, the Bank completed asset purchases of £200bn (QE1) and £125bn (QE2) respectively.  The decision to resume purchases in July 2012 will mean that by November 2012 the Bank will have bought a total of £375bn of assets, equivalent to around 25% of annual GDP.  This paper reviews the transmission channels through which asset purchases operate and assesses the impact of QE1 and QE2 on financial markets. 

Date: Tuesday 6th November, 17:00 - 18:00

Event Location: Barbara White Room, Newnham College

Title: A general theory of the firm

Abstract:

We develop a general theory of the firm that models investment and financing decisions simultaneously. Equity holders maximise shareholder value over an infinite time horizon through selecting optimal time paths of capital stock. Growth in capital stock is subject to investment constraints determined by the availability of internal and external finance. In order to reach the steady state faster and maximise value, equity holders can select debt and equity issues. The firm's investment decision and exogenous price shocks influence cash flows. Hence, the firm exhibits default risk due to exogenous shocks and investment decisions.

Debt holders select the debt ceiling, which defines the firm's debt capacity, to control their exposure to default risk. Cost of debt is determined on the market for external finance and reflects default risk.

The model shows that capital structure affects firm value if the firm has not reached its steady state. In the absence of information asymmetry, the model establishes a pecking order of internal and external finance. Once the firm approaches its steady state, the model converges to the classic Irrelevance Theory. Hence, the model is a general theory of the special case described by Modigliani and Miller (1958).

Date: Tuesday 20th November, 17:00 - 18:00

Event Location: Barbara White Room, Newnham College

Title: Regulatory arbitrage and cross-border bank acquisitions

Abstract:

We study how differences in bank regulation influence cross-border bank acquisition flows and share price reactions to cross-border deal announcements. Using a sample of 5,125 domestic and 793 majority cross-border deals announced between 1995 and 2008, we find evidence of a form of “regulatory arbitrage” in that cross-border bank acquisition flows involve primarily acquirers from countries with stronger supervision and stricter capital requirements than those of their targets. However, we also show that target and aggregate abnormal returns around the deal announcements are higher when acquirers come from countries with more restrictive bank regulatory environments even after accounting for the acquirer’s other attributes. These market reactions are consistent with a more benign form of “regulatory arbitrage” than one that is associated with a potentially destructive “race to the bottom” in which national bank regulators become less able to constrain excess risk-taking.

Date: Tuesday 22nd January, 17:00 - 18:00

Event Location: Sidgwick Hall, Newnham College

Title: Structural liquidity: Time coordination of economic activities and sectoral interdependence

Abstract:

Investigating the links between the financial and real spheres of the economy is especially relevant during crises. In this paper we concentrate on how liquidity impacts the real economy. Such impact is usually discussed in terms of microeconomic decision making (liquidity as a feature of portfolio management) and macroeconomic policy making (liquidity provision as an outcome of policy choice). What is generally missing is the analysis of liquidity mechanisms at intermediate levels of aggregation. Yet it is at the level of the interdependencies between economic sectors that liquidity arrangements are of central importance in determining the overall performance of any given economic system. This paper outlines a conceptual framework for structural liquidity analysis with the aim of overcoming the micro-macro divide. The strategy of the paper is as follows. First, we call attention to liquidity as a feature of the relationships between economic sectors: economic systems are more or less liquid depending on the degree of flexibility between sectors that the system’s architecture allows. Second, we emphasize that different sectors have different liquidity requirements (short-term versus long-term liquidity) depending upon the composition of their respective capital stocks (as expressed by the relationship between fixed and circulating capital). Finally, we draw some political-economic implications of our framework. As a result of their liquidity requirements, different sectors might have different interests in terms of the liquidity policies adopted by national or supranational authorities. This suggests another route to explaining the formation of decisions concerning liquidity in an economy – one that is based on the patterns of interdependencies among sectors and asymmetries in the composition of capital stocks.

Date: Tuesday 5th February, 17:00 - 18:00

Event Location: Barbara White Room, Newnham College

Title: How Likely is Contagion in Financial Networks?

Abstract:

Interconnections among financial institutions create potential channels for contagion and amplification of shocks to the financial system. We propose precise definitions of these concepts and analyze their magnitude. Contagion occurs when a shock to the assets of a single firm causes other firms to default through the network of obligations; amplification occurs when losses among defaulting nodes keep escalating due to their indebtedness to one another. Contagion is weak if the probability of default through contagion is no greater than the probability of default through independent direct shocks to the defaulting nodes. We derive a general formula which shows that, for a wide variety of shock distributions, contagion is weak unless the triggering node is large and/or highly leveraged compared to the nodes it topples through contagion. We also estimate how much the interconnections between nodes increase total losses beyond the level that would be incurred without interconnections. A distinguishing feature of our approach is that the results do not depend on the specific topology: they hold for any financial network with a given distribution of bank sizes and leverage levels. We apply the framework to European Banking Authority data and show that both the probability of contagion and the expected increase in losses are small under a wide variety of shock distributions. Our conclusion is that the direct transmission of shocks through payment obligations does not have a major effect on defaults and losses; other mechanisms such as loss of confidence and declines in credit quality are more likely sources of contagion.

Date: Tuesday 19th February, 17:00 - 18:00

Event Location: Barbara White Room, Newnham College

Title: Robust calibration of models in finance

Abstract:

We introduce a calibration concept for models in mathematical finance which uses information from time series and derivatives' prices simulatenously, namely to estimate model parameters being invariant under equivalent measure changes from time series data. Additionally these calibration procedures are less complex, more stable and allow for model rejection. For the estimation of invariant parameters we propose Fourier analysis inspired estimators due to some remarkable properties.

Join Professor Josef Teichmann for wine and canapes in the Centre for Mathematical Sciences after the seminar.

Josef Teichmann is Professor for Mathematical Finance at ETH Zurich. He holds a PhD on Global Analysis from Vienna University. For more than ten years he has been working in mathematical Finance in, e.g., term structure problems or computational aspects of finance.

Date: Tuesday 5th March, 17:00 - 18:00

Event Location: Room MR2, Centre for Mathematical Sciences, Cambridge University

This event was sponsored by Cantab Capital Partners.

Title: Long Memory Affine Term Structure Models

Abstract:

We develop a Gaussian discrete time, essentially affine term structure model which allows for long memory. This feature reconciles the strong persistence observed in nominal yields and inflation with the theoretical properties of affine models, especially for long maturities. We discuss how long memory can naturally arise with respect to the term structure of interest rates, providing a theoretical underpinning. We estimate a two factor version of the model whereby the factors have a clear economic interpretation as real short rate and expected inflation. We find that extension to long memory factors gives a substantial improvement, with respect to conventional models, in terms of model fit and forecast errors. Specifically, it seems crucial to model the expected inflation factor as a long memory process, while we do not find evidence of high persistence in the real rate dynamics. The model carries closed-form expressions for the term structure of real interest rates, real and nominal risk term premia, and inflation risk premia. All these quantities are time varying. An accurate in-sample as well as out-of-sample analysis of the model performance is presented.

Date: Tuesday 30th April, 17:00 - 18:00

Event Location: Barbara White Room, Newnham College

Title: No good deals - no bad models

Abstract:

Faced with the problem of pricing complex contingent claims, an investor seeks to make his valuation and hedging  robust to model uncertainty.  Our approach to this problem combines the “No Good Deals" methodology of Cochrane and Saa-Requejo [2000] with elements of the robustness framework of Hansen and Sargent [2008] and of Maenhout [2004]. The analysis introduces the notion of a model uncertainty induced utility function and shows how model uncertainty increases an investor's effective risk aversion. The presence of (and aversion to) model uncertainty gives greater weight (i.e. greater than the investor's marginal utility) to states in which losses are relatively large. Further, static hedging, (i.e. hedging an option by taking a “buy-and-hold" position in other assets, as opposed to dynamic hedging with the underlying asset), may become a relatively attractive hedging strategy in the presence of model uncertainty. We illustrate the methodology using some numerical examples.

Date: Tuesday 14th May, 17:00 - 18:00

Event Location: Sidgwick Hall, Newnham College

Title: What Have Physicists Accomplished in Economics?

Abstract:

Since roughly the mid 90's there has been an invasion of physicists into economics, and finance in particular.  In this talk I will give an idiosyncratic review of what physicists have accomplished since then.  I will argue that the biggest differences are epistemological, i.e. in the questions that are asked, how they are answered, the type of solutions that are considered useful, and the type of assumptions that are considered plausible.  I will present an overview of the main accomplishments, but focusing on a few areas, in particular order flow and market impact.  Time permitting I will make some remarks about high frequency trading:  In particular I will argue that having a proper understanding of market impact can be used to show that obtaining good position in the limit order book is worth hundreds of billions of dollars a year globally, and that simply changing the rules for execution easily eliminates this.

Date: Tuesday 28th May, 17:00 - 18:00

Event Location: Sidgwick Hall, Newnham College

Title: Innovation, Spillovers and Venture Capital Contracts

Abstract:

Innovative start-ups and venture capitalists are highly clustered, benefiting from localized spillovers: Silicon Valley is perhaps the most successful example. There is also substantial geographical variation in venture capital contracts: California contracts are more "incomplete". Could there be a causal link between regional differences in contract design, spillovers, and differences in performance? I explore this possibility, focusing on one observed contractual difference: California contracts typically contain fewer contingencies linking entrepreneurs’ rewards to explicit performance benchmarks. I find that in the presence of significant spillovers, it becomes optimal for innovative start-ups and their financiers to choose such contracts: the contracts maximize their ability to extract (part of) the surplus they generate through positive spillovers. This relaxes ex-ante financing constraints and makes it possible to induce higher innovative effort, generating further spillovers.

Date: Tuesday 11th June, 17:00 - 18:00

Event Location: Sidgwick Hall, Newnham College