Talks (titles and abstracts)
Alex Backwell: Hedging Evidence for Unspanned Stochastic Volatility
This research is concerned with resolving the empirical unspanned stochastic volatility (USV) question from a hedging point of view. We conduct an empirical hedging back-study based on cap and yield curve data. We also include data simulated from two benchmarks models, which each have a USV and non-USV version. We find that the hedging results are not directly informative vis-a-vis the presence of USV, and using our simulated data, we show that the hedging results found in previous papers are compatible with both USV and non-USV models. We develop a two-tier regression test that isolates hedging errors relating to volatility, and, with support from the simulation experiments, find strong evidence that USV is present in our dataset.
Stéphane Crépey: Capital Valuation Adjustment and Funding Valuation Adjustment
In the aftermath of the financial crisis, regulators launched in a major effort of banking reform aimed at securing the financial system by raising collateralisation and capital requirements.
Notwithstanding finance theories according to which costs of capital and of funding for collateral are irrelevant to decisions, banks have introduced an array of XVA metrics to precisely quantify them. In particular, KVA (capital valuation adjustment) and FVA (funding valuation adjustment) are emerging as metrics of key relevance.
In this paper we frame XVA metrics within a consistent model for the capital structure of a bank. We do not postulate that markets for contingent claims are complete. The fact that a bank is intrinsically leveraged, invalidates several of the conclusions of Modigliani-Miller theory but not all. We introduce a framework for assessing KVA, reflect it into entry prices and distribute it gradually to the bank's shareholders through a dividend policy that would be sustainable even in the limit case of a portfolio held on a run-off basis, with no new trades ever entered in the future. Our FVA is defined asymmetrically since there is no benefit in holding excess capital in the future. We notice that capital is fungible as a source of funding for variation margin (but not for initial margin), causing a material reduction in the FVA numbers.
Christa Cuchiero: Cover's universal portfolio in stochastic portfolio theory
We adapt Cover's universal portfolio approach to the setting of stochastic portfolio theory by considering – instead of constant rebalanced portfolios – portfolio maps being a function of the current market weights. For ergodic Markov diffusions we establish equality of the asymptotic performance among the best retrospectively chosen portfolio, the universal portfolio and the log-optimal portfolio.
Mario Giuricich: Stable Lévy motion approximation in catastrophe bond pricing
One of the most commonly used approaches for the pricing of index-linked catastrophe (CAT) bonds assumes that the underlying index follows a compound Poisson process. We briefly describe the structure of such CAT bonds. Moreover, pricing formulae based on such a process have been derived, but we note that they are difficult to compute both analytically and numerically. So, we present a method to weakly approximate the compound Poisson process by employing alpha-stable Lévy motion. A numerical example based on US insurance catastrophe loss data in such a context is presented and briefly discussed.
Thomas Krabichler: Term Structure Modelling in the presence of Multiple Yield Curves - An FX-like Approach
The aim of the talk is to present applicable results for pricing and hedging interest-rate-sensitive contingent claims in the presence of multiple yield curves. The model in consideration is a financial market with zero-coupon bonds that are exposed to credit and liquidity issues. The proposed studies interpret the risky zero-coupon bonds as a conversion of foreign default-free counterparts into the domestic market. The rate coincides with the current recovery rate of a domestic defaultable zero-coupon bond with an infinitesimal maturity. Liquidity constraints imply the emergence of two different pricing regimes for foreign zero-coupon bonds. One term structure corresponds to market prices, the other captures intrinsic economic values. The latter are determined utilising a natural numéraire that is inferred from the underlying itself. As the case may be, a change of numéraire in the classical sense is ineligible to the extent that it introduces arbitrage opportunities. Though, they cannot be exploited due to liquidity constraints. The vigorousness of the concept is underpinned by a flexible and parsimonious way to model the post-crisis interbank market.
Martin Larsson: Polynomial jump-diffusion models and their jump specifications
A jump-diffusion process is called polynomial if its extended generator maps polynomials to polynomials of the same or lower degree. Many fundamental stochastic processes, for instance affine processes, are polynomial, and their tractable structure makes them useful in a wide range of areas such as interest rates, credit risk, variance swaps, stochastic portfolio theory, etc. In this talk I will first give a brief introduction to polynomial jump-diffusions and how they can be used for financial modeling. Then, I will discuss some recent and ongoing work regarding jump specifications for polynomial jump-diffusions. In particular, I will illustrate the remarkably diverse behavior that arises beyond the diffusion case, including phenomena such as non-uniqueness of solutions to the martingale problem, and jump intensities with countably many poles. Nonetheless, a number of interesting structural properties can be established, and useful parametric sub-classes can be identified.
Andrea Macrina: Computation of price sensitivities by adjoint algorithmic differentiation
In this presentation, we report recent developments in the application of adjoint algorithmic differentiation for fast and efficient computations of price sensitivities. Tests have been performed on credit portfolios, American-style options, and efforts have been made to extend the methodology to the computation of counterparty-risk valuation adjustments.
Obeid Mahomed: Asset Pricing in Emerging Markets
Most asset pricing models are built with liquid developed markets in mind, where there is access to complete, or almost complete, pricing information. This is not the case for emerging economies, where one has to deal with illiquid financial markets. This talk will show how one may leverage econometric techniques to build asset pricing models for illiquid interest rate and equity markets.
Tom McWalter: Recursive Marginal Quantization of the Milstein Scheme
Recursive Marginal Quantization of the Euler scheme has recently been proposed by Sagna and Pagès (2015) as an efficient numerical method for the solution of stochastic differential equations. This method involves an algorithm that recursively quantizes the conditional marginals of the discrete Euler diffusion process. The main innovation in their work was to show that this approach converges. By generalizing their formulation, we show that it is possible to provide a recursive marginal quantization of the Milstein scheme. It is well known that this scheme converges with strong order
γ = 1, making it a better scheme for pricing path dependent options than the Euler scheme, which has strong order of γ =½. To illustrate performance we provide numerical comparisons of the two schemes. Initially, we directly compare the marginal density generated by the quantizer with the known transition density at each successive time step for the log-normal, square-root and CEV processes. This graphically demonstrates the improved performance of the Milstein scheme at initial time steps in the discretization. Both schemes are then used to price barrier options under a local-volatility model, thereby allowing performance comparisons. Finally, without providing full details, we indicate that it is, in principle, possible to perform recursive marginal quantization on other Itô-Taylor schemes.
Gareth Peters: Stress-testing European sovereign yield curves using liquidity and credit factors
Stress testing is an integral risk management tool for quantifying the size of potential losses under extreme stress events, and for identifying the scenarios under which such losses might occur. Stress testing has increased its popularity over the past years, especially after the 2007-2008 financial crisis, and has become an integrated risk management tool for banks, financial firms and central banks worldwide. This risk management tool has been strengthened even further in the Basel III accord (Basel Committee on Banking Supervision, 2010a). In March 2013, the Financial Policy Committee (FPC) recommended that regular stress testing of the UK banking system should be developed to assess the system’s capital adequacy. As a result, UK banks are required to perform stress tests to identify scenarios that could result in significant adverse outcomes and thus set regulatory capital requirements accordingly.
Moreover, central counterparties (CCPs) employ stress tests to determine the size of their default funds while brokerage firms and hedge funds conduct stress testing to calculate portfolio sensitivities, set portfolio limits and evaluate risks where Value-at-Risk (VaR) models are of limited use. Central banks also use stress testing, inter alia, to guide policy on the setting of prudential capital buffers or to guide on unconventional monetary policy interventions. In this study, we focus on a multi-curve setting and develop a modeling framework that can generate consistent cross-country stress test scenarios allowing for significant spillover effects between the economies. In particular, we model jointly the temporal and cross-country dependence structure of several European sovereign yield curves and associate movements in the yields and cross-country spreads with movements in macroeconomic and financial variables as well as market-wide and country-specific measures of liquidity and credit quality. The model is flexible enough to accommodate multiple scenarios contemporaneously and thus a large number of consistent scenarios across the curves being modeled can be generated. Moreover, we incorporate observable macroeconomic and financial variables into the modeling specification in a statistically rigorous way. This allows the study of interaction between macroeconomy and term structure and the assessment of importance and impact of these factors in the evolution.
Ralph Rudd: Pathwise Quantization of the SABR Model
In the current environment of negative rates, a multitude of numerical methods have been introduced for the SABR model and its various extensions. In this paper, we start by adding a new reduced-variance Monte Carlo technique to these numerical methods. This is illustrated on the traditional SABR model, see Hagan et al. [2002]. The method is based on the recursive marginal quantization of the asset price process using a sample path of the volatility. Therefore, we call this general technique the pathwise marginal quantization. A mathematical description as well as detailed examples are presented.
In addition we present some new approximation formulas for the free-boundary SABR model and a PDE technique. The latter two techniques can be used to test the goodness of the integration technique for this model in a recent publication by Antonov et al. [2015].
Josef Teichmann: Affine processes and non-linear PDEs
Affine processes have been used extensively to model financial phenomena since their marginal distributions are very tractable from an analytic point of view (up to the solution of a non-linear differential equation). It is well known by works of Dynkin-McKean-LeJan-Sznitman that one can turn this around and represent solutions of non-linear PDEs by affine processes. Recent advances in mathematical Finance in this direction have been contributed by Henry-Labordere and Touzi. We shall provide some general theory in this direction from the affine point of view. (Joint work with Georg Grafendorfer and Christa Cuchiero)