Quantitative Finance

Speaker(s)

• Agostino Capponi (Purdue University)
• Yong Zeng (University of Missouri, Kansas City)
• Tim Siu-Tang Leung (Columbia University)
• Hedibert Freitas Lopes (University of Chicago)
• Rafael Mendoza-Arriaga (University of Texas, Austin)
• José Figueroa-López (Purdue University)
• Cheng Ouyang (University of Illinois, Chicago)
• Olympia Hadjiliadis (Brooklyn College and Graduate Center CUNY)
• William Speth (Chicago Board of Options Exchange)
• Matthew Reimherr (University of Chicago)

Description

The quantitative study of uncertainty in finance is decades old, with mathematical underpinnings that trace back to the work of Bachelier in 1900. The last 15 years have seen extraordinary development of probabilistic and statistical tools for the study of stock markets and investment finance, aided by the new availability of powerful computational platforms and data streams which increase in frequency and volume. Some of the most established current foci in quantitative finance include the stochastic theory of absence of arbitrage, and the time series analysis of financial econometrics. In the former, Brownian motion and other continuous-time processes are used to study derivative pricing and extensions to incomplete markets and insider trading, while in the latter, volatility modeling in empirical finance helps understand value-at-risk and many other portfolio risk management tools. 

These two dominant tool-sets do not typically coexist in modern treatments. This session will foster an environment in which this gap can be addressed, by bringing in world-class specialists and new and rising researchers representing these diverse points of view. Other emerging directions, such as market microstructure, high-frequency finance, statistical inference for stochastic finance, and the study of market crashes, will further expand the scope of this wide-reaching workshop. 

Schedule

Fri, June 22 - Location: STEW 310

Time	Speaker	Title
8:30 - 8:55AM	Agostino Capponi	Default and Systemic Risk in Equilibrium
	Abstract: We develop a finite horizon continuous time market model, where risk averse investors maximize utility from terminal wealth by dynamically investing in a risk-free money market account, a stock, and a defaultable bond, whose prices are determined via equilibrium. We analyze the endogenous interaction arising between the stock and the defaultable bond via the interplay between equilibrium behavior of investors, risk preferences and cyclicality properties of the default intensity. We find that the equilibrium price of the stock experiences a jump at default, despite that the default event has no causal impact on the underlying economic fundamentals. We determine how heterogeneity of preferences affects the exposure to default carried by different investors.
9:00 - 9:25	Yong Zeng	Bayes Estimation via Filtering Equation for Partially-observed Heston Stochastic Volatility Model with Marked Point Process Observations
	Abstract: Heston's stochastic volatility (SV) model has been well studied and is regarded as a benchmark model in finance literature. Time-stamped transactions price data are marked point process (MPP) observations. This talk first reviews a general partially-observed framework of Markov processes with MPP observations recently proposed for UHF data; the posterior distribution and the filtering equation, which is a stochastic partial differential equation(SPDE) with recursiveness; and the Bayes Estimation via Filtering Equation (BEFE). In the past few years, Graphics Processing Units (GPUs) evolved from rendering graphics (linear algebra-like computations) for electronic games and video applications to becoming low-cost and green supercomputing units. With harnessing the newly available GPU supercomputing power in mind and targeting the SV model, we develop a new uniformly consistent recursive algorithm via BEFE for propagating and updating the joint posterior distributions. We show that the recursive algorithm is well suited for GPU computing and we present simulation and empirical results to demonstrate that the recursive algorithm works. Real time volatility track and feed is made possible. This is a joint work with Brent Bundick in Boston College.
9:30 - 9:55	Tim S.T. Leung	Derivatives Trading under Risk-Neutral and Risk-Averse Pricing Rules
	Abstract: We study the problem of optimal timing to buy/sell derivatives by risk-averse and risk-neutral agents in incomplete markets. In the risk-averse case, we adopt the indifference pricing mechanism to investigate the investor's timing of trades. This leads to a stochastic control and optimal stopping problem that combines the observed market price dynamics and the agent's risk preferences. In the zero risk-aversion limit, we observe a phenomenon where the investor and the market are pricing under different equivalent martingale measures. This motivates a formulation of price discrepancy in a general incomplete market. Moreover, we introduce the delayed purchase premium to characterize the optimal purchase/liquidation strategies. Numerical illustrations are provided for both equity and credit derivatives.
10:00-10:30AM	Break
10:30 - 11:15	Hedibert Freitas Lopes	Stochastic volatility models via particle methods
	Abstract: This talk reviews the main advances, over the last two decades, in the particle filter (PF) literature for dynamic models. We start with the bootstrap filter (BF) of Gordon, Salmond and Smith (1993) and the auxiliary particle filter (APF) of Pitt and Shephard (1999), since these two filters form the basis of most contributions to the PF literature. Both filters are then extended to accommodate sequential parameter learning, an area that has gained renewed attention over the last couple of years. We review the well-known Liu and West's (2001) and Storvik's (2002) filters, as well as Carvalho, Johannes, Lopes and Polson's (2010) particle learning (PL). We also discuss particle degeneracy, particle smoothing, sequential model comparison and the interface between PF and MCMC. The article is mainly intended for those researchers and practitioners with little or no practical experience with PF and are looking for a hands-on approach to the subject. In what in mind, we implement and compare the discussed particle filters in two well known contexts: the AR(1) plus noise model and the stochastic volatility model with AR(1) dynamics, or simply SV-AR(1) model. The AR(1) plus noise model is used since all sequential distributions are available in closed-form when parameters are kept fixed. Besides, many standard MCMC tools are available for this model and will be useful when proposing particle filters for this class of models. The SV-AR(1) model is a Gaussian dynamic model whose state evolves linearly and normally but its relation to the observation is nonlinear. Despite its deceiving simplicity, this model has proven to be challenging to estimate both via SMC as well as Markov chain Monte Carlo (MCMC) methods.
11:15-11:30AM	Break
11:30 - 11:55	Rafael Mendoza-Arriaga	Positive Subordinate CIR Processes with Two-Sided Mean-Reverting Jumps and Default Correlation and Clustering
	Abstract: In this talk we present the SubCIR jump-diffusion process. The SubCIR's diffusion dynamics are those of a CIR process. The SubCIR's jump component includes two-sided mean-reverting (state-dependent) jumps. The process remains strictly positive if the CIR process satisfies Feller's condition. The analytical tractability of the SubCIR process makes it a richer extension to the CIR process (compared to previous models) and it is also a natural alternative for interest rates and credit models. We further extend this model to the multivariate case in order to produce correlated defaults where it is possible to capture the so-called "default clustering effect".
12:00-1:30PM	Lunch
1:30 - 1:55	José Figueroa-López	Small-time asymptotics of stopped Lévy bridges and simulation schemes with controlled bias
	Abstract: In this talk, we characterize the small-time asymptotic behavior of the exit probability of a Lévy process out of a two-sided interval, conditionally on the terminal value of the process. In particular, we identify the leading term and a precise computable error bound. As an important application, we develop a novel adaptive discretization scheme for the Monte Carlo computation of functionals of killed Lévy processes with controlled bias. The considered functionals appear in several domains of mathematical finance such as structural credit risk models, pricing of barrier options, and contingent convertible bonds. The proposed algorithm works by adding discretization points sampled from the Lévy bridge density to the skeleton of the process until the overall error for a given trajectory becomes smaller than the maximum tolerance given by the user. This is a joint work with Peter Tankov (Université Paris-Diderot Paris 7, France).
2:00 - 2:25	Cheng Ouyang	Small-time expansions for local jump-diffusion models with infinite jump activity
	Abstract: We consider a stochastic differential equation driven by a Levy process Z and an independent Wiener process W. Under some regularity conditions, including non-degeneracy of the diffusive and jump components of the process as well as smoothness of the Levy density of Z, we obtain a small-time second-order polynomial expansion for the tail distribution and the transition density of the solution to such stochastic differential equations. As an application, the leading term for out-of-the-money option prices in short maturity under a local jump-diffusion model is derived. This is a joint work with José E. Figueroa-López.
2:30 - 2:55	Olympia Hadjiliadis	The price of a market crash and drawdown insurance
	Abstract: Drawdowns are path-dependent measures of risk and have been used extensively in the description of market crashes. We evaluate the market price of a market crash as measured through drawdowns by considering an investor who wishes to insure herself against the risk of a market crash and does so by purchasing insurance claims against drawdowns. We further examine the fair valuation of drawdown insurance in the possibility of early cancellation and identify optimal cancellation strategies. In particular, we demonstrate that the optimal exercise time in the case the swap contract is callable for a fixed fee is also drawdown related.
3:00-3:30PM	Break
3:30 - 4:15	William Speth	Volatility Trading: Fundamental Concepts, Products and Strategies
	Abstract: Today, most of the volatility trading worldwide is done with VIX futures and options, averaging over 100 MM vega daily and notional vega exposure of open interest close to 1 Billion. There are also 42 Exchange-Traded Funds and Notes linked to VIX with assets of 5 Billion. Some say volatility is an asset class, but volatility trading is complex and it is critical to understand what it means to trade 'pure' volatility and the nuances of volatility products that create opportunities and drive trading strategies.
4:15-4:30PM	Break
4:30 - 4:55	Matthew Reimherr	Predictability of Shapes of Intraday Price Curves
	Abstract: We develop a statistical framework, based on functional data analysis, for testing the hypothesis of the predictability of shapes of intraday price curves. We derive test statistics based on signs of the scores of the functional principal components. We establish its asymptotic properties under the null and alternative hypotheses, and demonstrate via simulations that it has excellent finite sample properties. A small empirical study shows that the shapes of the intraday price curves of large US corporations are not predictable.   This is joint work with Piotr Kokoszka.