by Matthew Ames (University College London)

The currency carry trade is the investment strategy that involves selling low interest rate currencies in order to purchase higher interest rate currencies, thus profiting from the interest rate differentials. This is a well known financial puzzle to explain, since assuming foreign exchange risk is uninhibited and the markets have rational risk-neutral investors, then one would not expect profits from such strategies. That is uncovered interest rate parity (UIP), the parity condition in which exposure to foreign exchange risk, with unanticipated changes in exchange rates, should result in an outcome that changes in the exchange rate should offset the potential to profit from such interest rate differentials. The two primary assumptions required for interest rate parity are related to capital mobility and perfect substitutability of domestic and foreign assets. Given foreign exchange market equilibrium, the interest rate parity condition implies that the expected return on domestic assets will equal the exchange rate-adjusted expected return on foreign currency assets. However, it has been shown empirically, that investors can actually earn arbitrage profits by borrowing in a country with a lower interest rate, exchanging for foreign currency, and investing in a foreign country with a higher interest rate, whilst allowing for any losses (or gains) from exchanging back to their domestic currency at maturity. Therefore trading strategies that aim to exploit the interest rate differentials can be profitable on average. The intention of this paper is therefore to reinterpret the currency carry trade puzzle in light of heavy tailed marginal models coupled with multivariate tail dependence features in the analysis of the risk-reward for the currency portfolios with high interest rate differentials and low interest rate differentials. To achieve this analysis of the multivariate extreme tail dependence we develop several parametric models and perform detailed model comparison.

Superposition of COGARCH processes

by Carsten Chong (Technische Universität München)

Stochastic volatility pricing models like the Lévy-driven Ornstein-Uhlenbeck process (also called the Barndorff-Nielsen & Shephard model), the more general Lévy-driven CARMA models or the continuous-time GARCH (COGARCH) models have synchronous price and volatility jump times.
In all these one-factor models jump sizes in volatility and price exhibit a fixed deterministic relationship. As this is not very realistic, multi-factor models are needed which can be provided by superpositions of the above models.  We suggest three different superpositions of COGARCH (supCOGARCH) volatility processes and corresponding price processes. Some distributional properties of volatility and price will be presented.
In particular, we find that the supCOGARCH models allow for more flexible autocovariance structures than the COGARCH. Moreover, other than the COGARCH model and other financial volatility models, the supCOGARCH processes do not exhibit a deterministic relationship between jumps of price and volatility processes. Simulations of volatilities and price processes will be shown for illustration.

Pricing & hedging asian-style options in energy

by Nils Detering (Frankfurt School of Finance & Management)

We solve the problem of pricing & hedging asian-style options on energy with a quadratic risk criterion when trading in the underlying future is restricted. Liquid trading in the future is only possible up to the start of the averaging period. After the start of the averaging period, the hedge positions can not be adjusted anymore until maturity. This reflects the trading situation in the nordic energy market NordPool. We show that there is a unique solution to this combined continuous-discrete quadratic hedging problem if the future price process is a martingale. Additionally the hedge positions before the averaging period are inherited from the market specification without trading restriction. As an application we consider three models and derive their quadratic hedge positions in explicit form, a simple Black Scholes Model with time-dependent volatility, the stochastic volatility model of Barndorff-Nielsen and Shephard and an additive exponential model.

Time-changed Brownian motion and option pricing

by Peter Hieber (Technische Universität München)

Time change models have become popular in Finance as they are analytically tractable and allow for a natural interpretation of the time-change as a measure of economic activity (’business time scale’, ’transaction clock’). Many well-known models can be represented as a time-changed Brownian motion covering not only Lévy-type models, but also regime-switching, Sato, or stochastic volatility models. We show that if the time-change is continuous, one can analytically price barrier contracts (for example (double) barrier options, (corridor) bonus certificates) via an efficient power series representation. This builds on the fact that in this model class one is able to derive the first-passage time in closed-form following Hieber and Scherer [2012]. Surprisingly, this result also turned out to be a very efficient approximation of European option prices for both continuously and discontinuously time-changed Brownian motion. Our approach avoids Fourier integrals and allows us to obtain a range of vanilla call prices in high accuracy (relative error <1e-8) and little time (<1 ms). We compare the results to its numerical alternatives, for example, Fast Fourier pricing (Carr and Madan [1999]), the COS method (Fang and Osterlee [2008]), or rational approximations (Pistorius and Stolte [2012]).

Inflation protected investment strategies

by Mirco Mahlstedt (Technische Universität München)

We present a dynamic inflation-protected investment strategy which is based on traditional asset classes and Markov-Switching models. Different stock market as well as inflation regimes are identified and within those regimes the inflation hedging potential of stocks, (corporate) bonds, real estate, commodities and gold are investigated. Within each regime, we determine optimal investment portfolios. An early warning system for stock market turbulences as well as turbulent inflation periods is proposed and adynamic inflation-protected investment strategy is developed, which combines inflation protection and upside potential.

Aligning different approaches for replicating portfolios

by Jan Natolski (Universität Augsburg)

The Solvency II directive requires that insurance companies hold sufficient reserves to be able to meet claims from policy holders in any year. The amount of reserves is determined on the basis of the market consistent value of the insurers liabilities. Naturally, the distribution of the future value of liabilities is therefore of interest to any insurance company. To this end, the construction of replicating portfolios has gained increasing attention in the life insurance sector. In current literature, two portfolio construction approaches have become the most popular. We show how the constructions are linked and discuss an alternative method to approximate the distribution of future liabilities using the Longstaff-Schwartz algorithm.

Nice Moment Swaps

by Johannes Rauch (University of Sussex)

We introduce an innovative class of financial derivatives with nice pricing and hedging properties. Based solely on the assumption of an arbitrage-free market we generalise the recent work of Anthony Neuberger on realised skewness, deriving a vector space of characteristics that satisfy the so-called aggregation property. A swap contract that is defined based on one of these characteristics can be perfectly replicated in discrete time and related to moments of the return distribution. The returns on these swaps are unbiased estimators for the associated risk premiums. Our framework therefore represents a great tool for discovering statistical arbitrage and identifying profitable option trading strategies. This is joint research with Carol Alexander.

Contagion effects and collateralized credit value adjustments for credit default swaps

by Lars Rösler (Vienna University of Economics and Business)

The paper is concerned with counterparty credit risk management for credit default swaps in the presence of default contagion. In particular, we study the impact of default contagion on credit value adjustments such as the BCCVA (Bilateral Collateralized Credit Value Adjustment) of (Brigo et al. 2012) and on the performance of various collateralization strategies. We use the incomplete-information model of Frey and Schmidt (2012) as vehicle for our analysis. We find that taking contagion effects into account is important for the effectiveness of the strategy and we derive refined collateralization strategies to account for contagion effects.

Bivariate semi-Markov Process for Counterparty Credit Risk

by Giovanni Salvi (Sapienza University of Rome)

We consider the problem of constructing an appropriate multi-variate model to study counterparty credit risk in the credit rating migration problem. For this nancial problem dierent multivariate Markov chain models were proposed. However the Markovian assumption may be inappropriate for the study of the dynamics of credit ratings, which typically show non-Markovian like behaviour. In this paper we develop a semi-Markov approach to study the counterparty credit risk by dening a new multivariate semi-Markov chain model. Methods are given for computing the transition probabilities, reliability functions and the price of a risky Credit Default Swap.

A two-sided Gamma-OU-BNS model for multicurrency FX markets

by Thorsten Schulz (Technische Universität München)

We present a multivariate jump diffusion model incorporating stochastic volatility and two-sided jumps for multicurrency FX markets, which is an extension of the univariate Gamma-OU-BNS model introduced by [Barndorff-Nielsen and Shephard, 2001]. The model can be considered a multivariate variant of the two-sided Gamma-OU-BNS model (cf. [Bannör and Scherer, 2013]). We discuss FX option pricing and provide a calibration exercise, modeling two FX rates with a common currency by a bivariate model and calibrating the dependence parameters to the implied FX volatility surface.

Pricing and Risk Management with Stochastic Volatility Using Importance Sampling

by Przemyslaw Stilger (Manchester Business School)

In this paper, we apply importance sampling to Heston's stochastic volatility model and Bates's stochastic volatility model with jumps. We propose an effective numerical scheme that dramatically improves the speed of importance sampling. Most importantly, we introduce the Likelihood Ratio Method Based on Characteristic Function to estimate the Greeks in a computationally efficient manner. To achieve significant variance reduction also for the Greeks, we combine this method with importance sampling. All results are illustrated using European and barrier options.

Change detection in a Heston type model

by Tamás Szabó (University of Szeged)

In the talk our main objective will be to define a process with the help of which we can introduce a change detection procedure for a special type of the Heston model. We will first introduce a change detection method for the Cox-Ingersoll-Ross process, which describes the volatility in the Heston model, and is easier to analyze. We will use the likelihood function to develop a testing procedure based on the score vector and the maximum-likelihood estimates. The null hypothesis is that the parameters are unchanged during the observations, and the alternative is that there is exactly one change. Asymptotic results are available under the null hypothesis and also under the alternative, supposing that the change occurs at a fixed proportion of the sample length. After these results, we will show how we can apply the same techniques to our Heston type model.

Calculation and Evaluation of an Intraday Value at Risk

by Florian Walla (University of Tübingen)

Calculating intraday VaR recently came into the focus of research. In this paper di_erent models for forecasting it are taken into account. While an ARMA-GARCH approach is used on the equally spaced grid, log-ACD models are applied on the unequally spaced grid. In addition to the normal innovation distribution which had a bad forecasting performance in the literature, a non-parametric and a t-distribution are used. The log-ACD models are transformed to an equally spaced grid for testing purposes. Extensive forecasting performance testing gives evidence that a log-ACD approach with a conditional t-distribution is at least on par with the wellknown ARMA-GARCH models as they both pass almost all tests successfully. There is weak evidence the log-ACD approach with the conditional t-distribution outperforms the ARMA-GARCH model.