Model Agnostic Financial Engineering

I am interested in building pricing models for derivatives flexible enough to capture all available statistical and pricing information as well as to embed views. For example, I am interested in the following:

Fixed income derivatives: how to account for the stochastic monetary policy process when pricing long dated fixed income derivatives? How to interpret the implied volatility skew as forecasts for future monetary policy? How to price Bermuda swaptions consistently with European swaptions accounting for the momentun of the rate process? How to model and risk manage callable CMS deals? How to structure and hedge CMS spreads?

Foreign exchange derivatives: how to model a rate process accounting for stochastic volatility and stochastic reversal? How to incorporate the effect of aggregate barrier positioning? How to correlate the foreign exchange process to monetary policy in either currency? How to reconcile barrier and European options accounting for the momentum of rates? How to price path dependent options such as range accruals and faders? How to calibrate long dated options accounting for interest rate risk?

Equity derivatives: how to build nearly time homogeneous processes which calibrate well to the implied volatility surface? How to correctly model vega convexity for long dated structures? How to structure long dated products? How to understand the coupling and de-coupling between credit and equity derivatives and price credit-equity hybrids? How to model the interplay between tail risk and risk of first loss?

Credit correlation structures: how to build and calibrate detailed bottom up models whereby the process for each reference name is described precisely and is not analytically tractable? How to assess the impact of volatility risk, spread dispersion and volatility dispersion? How to price and hedge concentration bespoke baskets and tranche options? How to risk manage portfolios of credit derivatives with consistent modeling assumptions?

Commodity derivatives: How to build models that reflect econometric evidence? How to price and risk manage complex derivatives such as swing options?

Risk management: How to configure an engineering solution to handle derivative portfolios consistently? Is it possible from the engineering standpoint to model each risk factor with a rich, realistic process which is used throughout derivative portfolios consistently?

To address these questions, in my work I tend to favor flexible semi-parametric, regime switching models. While standard single regime models tend to be in a state of flux as they need to be constantly recalibrated as market conditions change, I do my best to incorporate the flux endogenously into the models by allowing for a number of different market regimes and the possibility to switch stochastically from one to another.

As one goes down this path, one soon encounters technical difficulties. One needs to use a suitable mathematical framework and build efficient engineering solutions. That is why I became interested in operator methods and constructive probability theory.