Talks

Prof. Laura Ballotta (Bayes Business School) 

Title: The term structure of implied correlations between S&P and VIX

Abstract: We develop a joint model for the S&P500 and the VIX indices with the aim of extracting forward looking market consistent information on the correlation between the two markets. We achieve this by building the model on time changed Lévy processes, deriving closed analytical expressions for relevant quantities directly from the joint characteristic function, and exploiting the market quotes of options on both indices. We perform a piece-wise joint calibration to the option prices to ensure the highest level of precision within the limits of the availability of quotes in the dataset and their liquidity. Using the calibrated parameters, we are able to quantify the ‘leverage/volatility feedback’ effect along the term structure of the VIX options and corresponding VIX futures. We illustrate the model using market data on SPX options and both futures and options on the VIX. This is joint work with Ernst Eberlein and Grégory Rayée.

Dr. Jorge Yslas Altamirano (University of Liverpool)

Title: Claim frequency modeling through phase-type mixture-of-experts regression

Abstract: In this talk, we address the problem of modeling loss frequency using regression when the counts have a non-standard distribution. We propose a novel approach based on mixture-of-experts specifications on discrete phase-type distributions. Compared to continuous phase-type counter parts, this approach offers fast estimation via expectation-maximization algorithms, making it more feasible for use in real-life scenarios. Our model is both robust and interpretable in terms of risk classes and can be naturally extended to the multivariate case through two different constructions. Using simulated and real-world data, we showcase how our approach provides an effective solution for modeling loss frequency in non-standard situations.

Prof. David Wilkie (University of York)

Title: Research that I have not yet done, but that I consider worth doing 

Abstract: This talk will discuss a collection of different ideas that have not yet been done but I believe are worth considering. 

Dr. Alet Roux (University of York)

Title: Higher order approximation of option prices in Barndorff-Nielsen and Shephard models

Abstract: I will present an approximation method based on the mixing formula for pricing European options in Barndorff-Nielsen and Shephard models. This approximation is based on a Taylor expansion of the option price. It is implemented using a recursive algorithm that allows us to obtain closed form approximations of the option price of any order (subject to technical conditions on the background driving Levy process). This method can be used for any type of Barndorff-Nielsen and Shephard stochastic volatility model. Explicit results are presented in the case where the stationary distribution of the background driving Levy process is inverse Gaussian or gamma, and the approximation compares favorably to option prices produced by the characteristic function. Time permitting I will present asymptotic results for the error of the Nth order approximation and error bounds in both cases. This talk is based on joint work with Alvaro Guinea Julia, recently published in Quantitative Finance.

Yukun Cao (University of Leeds)

Title: Exit Game with Asymmetric Information

Abstract: With the development of technology, it is common that once a prosperous industry declines and eventually vanishes. Companies and players in these industries need to choose the right time to exit the market.  Generally, firms cannot know their opponents' exit value a priori. Hence, they need to 'learn' this information from their opponents' behaviour in the market. In this talk, we will use a non-zero-sum stochastic game to model the behaviour of the firms in this situation.

Cedric Koffi (University of Liverpool)

Title: Impact of social factors on loan delinquency in microfinance

Abstract: In this work, we develop multistate models to analyse loan delinquency in the microfinance sector, using data from Ghana. The models are designed to account for both partial repayments and the short repayment durations typical in microfinance, focusing on estimating the probability of transitions between two or three repayment states, including delinquency. Social variables, such as religious and cultural factors, were found to play a statistically significant role in influencing repayment behavior, highlighting the impact of societal dynamics on financial outcomes. We explored both time-independent and time-dependent frailty models to capture unobserved heterogeneity. Overall, the findings emphasize the importance of social factors in delinquency but suggest limited predictive gains from incorporating frailties into multistate models.

Luis M Chaparro J (University of Leeds)

Title: Euler scheme for SDEs with distributional drifts

Abstract: We study numerical solutions for SDEs with the drift being a generalised function taking values in a Hölder-Zygmund space of negative regularity.

We design an Euler-Maruyama scheme and prove a bound for the strong rate of convergence in $L^1$ for a class of SDEs and a class of McKean SDEs.

Finally, we present some results on the implementation of the scheme.

This is a joint work with Elena Issoglio (University of Turin) and Jan Palczewski (University of Leeds).

Noah Beelders (University of Liverpool)

Title: Probabilistic Cauchy functional equations

Abstract: In this presentation, I shall introduce the notion of a probabilistic Cauchy functional equation (PCFE), which are functional equations of the following form:

             f(X_1 + X_2) =_d f(X_1) + f(X_2),

for two independent identically distributed random variables X_1 and X_2 with appropriate support. When X_1 and X_2 are exponentially distributed, we provide sufficient regularity conditions on the function f to ensure that the unique measurable solution to the above equation is solely linear. Furthermore, we present some partial results in the general case establishing a connection to the integrated Cauchy functional equations.

Dr. Lanpeng Ji (University of Leeds)

Title: Bayesian CART models for aggregate claim modeling

Abstract: In this talk, we discuss some Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We first introduce a general framework for the BCART models applicable to data with multivariate responses, which is particularly useful for the joint BCART models with a bivariate response: the number of claims and aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data by using various distributions. We discover that the Weibull distribution is superior to gamma and lognormal distributions, due to its ability to capture different tail characteristics in tree models. Additionally, we find that sequential BCART models and joint BCART models, which incorporate dependence between the number of claims and average severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is assumed. The effectiveness of these models' performance is illustrated by carefully designed simulations and real insurance data.