Bayesian Inference for Diffusion Processes from Partial Observations and Expectations

A substantial amount of publicly available datasets represent educated predictions on the evolution of stochastic processes. These include financial derivative instruments, such as option prices, that can be formulated as expectations of the underlying price process. The proposed project considers models with latent diffusion processes that can be linked to direct observations, but also to such conditional expectations. The goal is to utilise advanced computational methods to estimate the data generating mechanism from both datasets. Moreover, to develop a general inferential framework to handle parameter and model uncertainty.

The main focus is on financial applications, and in particular estimating stochastic volatility models estimated from asset and option prices. In this context, the procedure may be viewed as a robust calibration technique for identifying the model driving the option prices while estimating the volatility and its parameters. This facilitates subsequent use for pricing financial derivatives and implementing hedging strategies. Desired features of the proposed methodology will include: applicability to various types of derivatives, accurate and controllable approximations of the intractable quantities in the model, and feasible computational schemes. Other objectives include developing and applying suitable procedures for specifying various aspects of the model in different observation settings, and generalising the existing computational framework to include jump diffusions, support Bayesian model choice and allow implementation in an online manner. The aim is also to develop a general inferential framework that will be able to accommodate applications from different areas. Specific examples in structural credit risk models, electricity markets and macroeconomics will be considered.

The proposed research include simulation based inference for diffusions with stochastic volatility, used for asset pricing. It is therefore expected that it will be beneficial for various academic disciplines such as Computational Statistics, Mathematical Finance and Econometrics. Moreover, as techniques for data calibration and hedging will be developed, it will also be of interest to the financial sector and power markets.

The results of this project will provide benefits for various research users.

Beneficiaries in the academia include researchers in the field of stochastic processes for tasks such as simulation and inference for their parameters. Also, academics in mathematical and quantitative finance, econometrics, computational statistics and scientists working in applications based on diffusion models. More details on the benefits of the researchers in these academic areas are provided in the academic beneficiaries section.

Beneficiaries outside academia include:

Financial institutions ranging from central banks to hedge funds: The proposed research will be of direct relevance for calibration of option pricing models, offering a rigorous and natural way to incorporate parameter and model uncertainty. Furthermore, it is expected to provide solutions in cases where calibration is difficult to achieve, like the volatility of volatility process. This in turn would lead to a robust estimation of pricing kernels, and will facilitate implementation of hedging strategies for e.g. variance options and swaps. Efficient and accurate estimation of volatility would also facilitate algorithmic trading strategies, for example by targeting or avoiding volatile periods. Contrasts of the volatility estimates from this project's model based approach with well known model-free indices, such as the volatility index (VIX) provided by the Chicago Board of exchange (CBOE), will also be of interest particularly in cases where volatility is traded. Overall, the proposed research is closely related with financial institutions and therefore linked with potential economic development.

Electricity markets: The fact that electricity cannot be stored economically has resulted to the development of specific types of contracts to maintain balance between supply and demand. These include short term contracts (spot), futures, forwards and in some cases path depended derivatives. They are traded extensively in power markets such as Nord Pool. The project will provide a general framework that can be used in a similar manner to asset prices for task such as calibration and hedging. Nevertheless, it will take into account specific features of the underlying electricity price process (seasonality and spikes) and derivatives thereof. This framework would be helpful to electricity traders and market makers.

Economists: The project will consider general equilibrium models for macroeconomic data (e.g. output and labour supply), to link to latent states such as capital and productivity level. The models will have stochastic volatility to capture shocks and structural changes and provide more accurate inference that can be combined with related economic theory.