American Option Pricing in a Tick -Calibration in a Click:                   

Andersen, Lake and Offengenden (2016) present a staggeringly fast and accurate method for the pricing of American options under constant parameter Black-Scholes assumptions. In this talk, we discuss the method, a few extensions including negative interest rates and prices, and its practical implementation and application to the estimation of implied dividends and volatility smiles from  American option prices. Issues around absence of arbitrage and asynchronous data is also discussed.

Price Excursions: a Novel Approach to Dynamic Trading Strategies:

The risk and return profiles of a broad class of dynamic trading strategies, including pairs trading and other statistical arbitrage strategies, may be characterized in terms of excursions of the market price of a portfolio away from a reference level. We propose a mathematical framework for the risk analysis of such strategies, based on a description in terms of price excursions. We show that this approach leads to model-free insights on the risk of many dynamic trading strategies and relates their properties to the properties of price paths.
Finally, we describe a non-parametric scenario simulation method for generating paths whose excursion properties match those observed in empirical data. We illustrate this approach in the case of pairs trading strategies for equities.

• Reference: 
  Ananova, Anna and Cont, Rama and Xu, Renyuan, Excursion Risk: https://ssrn.com/abstract=3723980 

IBOR Transition: Looking Forward to Backward-Looking Rates:

In this talk, we define and model forward risk-free term rates, which appear in the payoff definition of derivatives and cash instruments, based on the new interest-rate benchmarks that will be replacing IBORs globally. We show that the classic interest-rate modeling framework can be naturally extended to describe the evolution of both the forward-looking (IBOR-like) and backward-looking (setting-in-arrears) term rates using the same stochastic process. We then introduce an extension of the LIBOR Market Model (LMM) to backward-looking rates. This extension, which we call generalized forward market model (FMM), completes the LMM by providing additional information about the rate dynamics between fixing/payment times, and by implying dynamics of forward rates under the classic money-market measure. Our FMM formulation is based on the concept of extended zero-coupon bonds, which proves to be very convenient when dealing with backward-looking setting-in-arrears rates. Thanks to this, not only the bonds themselves, but also the forwards and swap rates, along with their associated forward measures, can be defined at all times, even those beyond their natural expiries.

Finally, we complete the FMM by embedding into a Markovian HJM to allow for the generation of any forward-looking or backward-looking rates, and hence for the pricing of any exotic payoff or derivatives portfolio.

Deep learning in finance: an empirical investigation:

We are interested in using deep learning methods in order to compute option prices and implied volatilities. We investigate numerically the effects of various parameters (functions, rates, architecture) in the efficiency of these methods. This is joint work with Jonas Papazoglou-Hennig (TU München) and Giorgos Papagopoulos (NTU Athens).

A New Version of Roger Lee’s Formula:

We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that when the underlying stock price martingale admits finite log-moments E[|log(S) |^q] for some positive q, the arbitrage-free growth in the left wing of the implied volatility smile is less constrained than Lee’s bound. The result is rationalised by a market trading discretely monitored variance swaps wherein the payoff is a function of squared log-returns, and requires no assumption for the underlying martingale to admit any negative moment. In this respect, the result can derived from a model-independent setup. As a byproduct, we relax the moment assumptions on the stock price to provide a new proof of the notorious Gatheral-Fukasawa formula expressing variance swaps in terms of the implied volatility.

 Quantitative Trading Strategies & Asset Pricing Using Machine Learning:

 Machine Learning (ML) and Predictive Analytics are now embedded in a broad variety of use cases in Quantitative Finance, from information extraction to sentiment analysis, from factor scoring models to complex instrument pricing methods, and from risk premium mining to portfolio construction models. ML is increasingly being used for asset pricing, e.g, option pricing or illiquid bond pricing where we need to learn the pricing function using data driven techniques as a further enhancement of methods rooted in stochastic modeling.

Quantitative traders and data scientists require automated ML & AI technologies to quickly extract actionable information from unstructured and increasingly non-traditional sources of data. We will illustrate the construction and use of such derived signals through novel use cases.

This talk will provide a brief overview of the following topics:

• The broad application of machine learning in finance: opportunities and challenges.
• Construction of scoring models and factors from complex data sets, including: News/Social Media, Supply Chain Network, Options Prices and ESG (Environmental, Social & Governance).
• Use of alternative data, such as extreme weather (i.e., cyclones, snowfall) to quantify the weather’s impact on companies that own retail stores and factories.
• Machine Learning techniques for asset pricing, enhancing complex quant models (i.e., PDE, Monte Carlo) for an efficient pricing of derivative securities and pricing of illiquid securities using data driven methods.

Poly Parrot:

We look at to Antoine Savine and Brian Huge’s work on differential machine learning for option pricing (presented on the 2020 MathFinance Conference), with the focus heavily on the differential part. We will replicate/copy/parrot their results in a simpler polynomial regression set-up and demonstrate how they help us in a hedging context. 

 Black Basket Analytics for Mid-Curves and Spread-Options

Business meets quant, meets crypto:

Toft presents the case for the switch from quantitative methods being used to analyze exchange rates to their use to create new exchange rates, and for their practical implementation as enabled by crypto on distributed ledger technology (DLT). The emergence of crypto-quant-solutions opens the door to a new chapter of more-stable, market-based exchange rates, from the approach of “developing the best number” rather than finding the best number among those already existing. The presentation focuses on the case of the Global Stability Unit www.GSU.io.

Developing FX Options Systematic Trading Strategies in Python:       

In our talk, we shall discuss how to analyse the FX vol market using Python, and in particular we shall show how we can develop systematic trading strategies for FX vanilla options and to backtest using the open source finmarketpy library using historical data.

Tools for Option Trading in a crazy world:

The listed equity options markets have by any number of metrics become very large, liquid, competitive, and sophisticated over the last decade. The current pandemic has led to many further remarkable features, from the “strange’’ — but perfectly rational — shapes in index and single stock vol surfaces, to changes in spot-vol dynamics, to the dramatic increase in retail participation and trading frenzies in meme stocks like GME. We discuss (i) some of the challenges this raises for valuation and hedging in an increasingly automated world for both vanilla and exotic options, (ii) the requirements for tools to help navigate this new world, and (iii) how these requirements are implemented in the Vola library.

Consistent Recalibration Models and Deep Calibration (joint work with Matteo Gambara):

Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives’ prices. Several approaches have been suggested to tackle this problem, but all of them, including CRC models, suffered from numerical intractabilities mainly due to the presence of complicated drift terms or consistency conditions. We overcome this problem by machine learning techniques, which allow to store the crucial drift term’s information in neural network type functions. This yields first time dynamic term structure models which can be efficiently simulated

Copula-Based Hedging of Cryptocurrencies:

We investigate different methods of hedging cryptocurrencies with Bitcoin futures.  The introduction of derivatives on Bitcoin, in particular the launch of futures contracts on CME in December 2017, allows for hedging exposures on Bitcoin and crytpocurrency indices, such as the CRIX. Because of volatility swings and jumps in Bitcoin prices, the traditional variance-based approach to obtain hedge ratios is infeasible.  The approach is therefore generalised  to various risk measures, such as value-at-risk, expected shortfall and spectral risk measures, and to different copulas for capturing the dependency between spot and future returns, such as the Gaussian, Student-t, NIG and Archimedean copulas. Various measures of hedge effectiveness in out-of-sample tests give insights in the practice of hedging Bitcoin and the CRIX.

This is joint work with Meng-Jou Lu (National University of Singapore) and Francis Liu (Berlin School of Economics and Law, Humboldt University Berlin).

Machine Learning and Option Pricing:

In computational Finance, numerical methods are commonly used for the valuation of Financial derivatives. These price models are often
multi-dimensional and heavy from the time consuming view point. Artificial Neural Networks (ANNs) with multiple hidden layer became
successful machine learning methods to evaluate Options and Risks from a large data set.

Estimating risk measures in the presence of heteroscedasticity with LSTM

The efficient estimation of risk is an important task to solve in practice. Recently, unbiased estimators have been proposed in Pitera & Schmidt and their excellent performance in backtesting was shown in the i.i.d. situation. In this talk we consider the case where we drop the i.i.d. assumption and allow for GARCH time series. An unbiased estimator in this situation is proposed and compared to existing other approaches. Most importantly, we employ an LSTM neural network as a universal tool for estimating risk in the presence of time series and compare their performance.

Martingale Modelling for the USDHKD Exchange Rate

The U.S. dollar / Hong Kong dollar foreign exchange rate is constrained by a peg maintained by the Hong Kong Monetary Authority.  The spot FX rate is allowed to move within a band with direct intervention by the Monetary Authority at the band limits.  We analyze the resulting FX dynamics and show that the options market anticipates a possibility of de-peg.  We present a martingale model incorporating reflection at the boundary to account for the intervention, with jump at the time of reflection compensating to achieve a martingale property.  We show the model captures features unique features of the market dynamics and present results for pricing and hedging vanilla and exotic options under our model.

 New fallbacks for derivatives linked to key interbank offered rates (IBORs) came into effect on January 25, ensuring a viable safety net is in place in the event an IBOR becomes permanently unavailable while firms continue to have exposure to that rate.

The fallbacks, published by the International Swaps and Derivatives Association, Inc. (ISDA), will be incorporated into all new derivatives contracts that reference ISDA’s standard interest rate derivatives definitions. They will also be included in legacy non-cleared derivatives if the counterparties have bilaterally agreed to include them or both have adhered to the IBOR Fallbacks Protocol. More than 12,000 entities across nearly 80 jurisdictions had adhered to the protocol as of January 25.

A Data-Driven Market Simulator for Small Data Environments:   

 In this talk we investigate how Deep Hedging brings a new impetus into the modelling of financial markets. While a DNN-based data-driven market generation unveils a new and highly flexible way of modelling financial time series, it is by no means “model-free”. In fact, the concrete modelling choice is decisive for the features of the resulting generative model. After a very short walk through historical market models we proceed to neural network based generative modelling approaches for financial time series. We then investigate some of the challenges to achieve good results in the latter, and highlight some applications and pitfalls. While most generative models tend to rely on large amounts of training data, we present here a parsimonious generative model that works reliably even in environments where the amount of available training data is notoriously small. Furthermore, we discuss how a rough paths perspective combined with a parsimonious Variational Autoencoder framework provides a powerful way for encoding and evaluating financial time series data in such environments. Lastly, we also discuss some pricing and hedging considerations in a DNN framework and their connection to Market Generation.

We will also discuss the usability of the developed techniques for outlier detection and market regime classification. The talk is based on joint work with H. Buehler, I. Perez Arribaz, T. Lyons and B. Wood, see: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3632431

Risk, Cost and Reward of Computing Risk:

“The trader known as the London Whale lost at least $6.2 billion for JPMorgan Chase & Co. in 2012.” Bloomberg News.

Did the London Whale have a risk report to base trading decisions on?

Did he use them? How much is a better Risk system really worth?

“With the new Maxeler technology, JPMorgan’s trading businesses can now compute orders of magnitude more quickly, making it possible to improve our understanding and control of the profile of our complex trading risk,” said Peter Cherasia, head of markets strategies at JPMorgan.” was published by Forbes Magazine on March 12, 2012, the same year the London Whale lost billions.

What is the risk of not computing risk? What is the risk of not computing risk to a sufficient level of accuracy, i.e. by not waiting for the Monte Carlo paths to converge? How about cost to maintain the software or rewrite it to faster and better technologies? How about the cost in terms of trading loss from not having computed event risk in real time? If AI companies are building AI chips, how about Finance companies investing into building Risk chips.

In this talk we will explore how the computing industry is supporting the Finance industry to reduce systemic risk while giving traders real time forward visibility.

“The trader known as the London Whale lost at least $6.2 billion for JPMorgan Chase & Co. in 2012.” Bloomberg News.

Did the London Whale have a risk report to base trading decisions on?

Did he use them? How much is a better Risk system really worth?

“With the new Maxeler technology, JPMorgan’s trading businesses can now compute orders of magnitude more quickly, making it possible to improve our understanding and control of the profile of our complex trading risk,” said Peter Cherasia, head of markets strategies at JPMorgan.” was published by Forbes Magazine on March 12, 2012, the same year the London Whale lost billions.

What is the risk of not computing risk? What is the risk of not computing risk to a sufficient level of accuracy, i.e. by not waiting for the Monte Carlo paths to converge? How about cost to maintain the software or rewrite it to faster and better technologies? How about the cost in terms of trading loss from not having computed event risk in real time? If AI companies are building AI chips, how about Finance companies investing into building Risk chips.

In this talk we will explore how the computing industry is supporting the Finance industry to reduce systemic risk while giving traders real time forward visibility.

 Moderator for the panel discussion on IBOR transition 

Implied Volatilities for Options on Backward-Looking Term Rates:

We derive valuation formulas for caps and floors on backward-looking term rates in the Black-1976, Bachelier and Hull-White-1-Factor models explicitly regarding valuation in the fixing period, extending and detailing results of [Lyashenko & Mercurio 2019, Henrard 2019, Turfus 2020]. These formulae facilitate us to provide a consistent definition for implied volatility on backward-looking term rates.