Title and Abstract

August 26No meeting

September 2Organizational meeting

September 9PCA100 - Kyounghee Kim, FSU

We will discuss the paper "Common Factors affecting bond returns" by Robert Litterman and José Scheinkman.

Related paper : "PCA Based Calibration of an HJM Model" by Roberto Renò and Adamo Uboldi.

September 16Global Sensitivity Analysis and Effective Dimension - Giray Ökten, FSU

September 23Pricing a Daily Option on Power - Motoi Namihira, FSUStandard option pricing theory relies on market completeness and the existence of a hedging instrument. In energy markets, due to the non-storability of power, the hedging assumption fails. This issue is particularly evident when pricing the daily option on power. In this talk we shall present one method of deriving a price consistent with market data.

September 30Calibration of local volatilities using Tikhonov regularization - Jian Geng, FSUCalibration is important in modeling because how successful a model works depends largely on the extent of successful calibration of its parameters. In this presentation, we attempt to calibrate the local volatility model, a deterministic volatility model to extend Black-Scholes constant volatility model, using SPX options.

Calibration of local volatilities using Tikhonov regularization

October 7An introduction to Fourier Transform and Option Pricing - Pierre Garreau, FSUThis paper introduces Fourier Transform methods for Option Pricing. I present the pricing problem and its dual in the context of a modelisation of asset returns thanks to random walks and their limits: infinitely divisible distributions. After a review of the Black-Scholes (BS) and Merton's Jump-diffusion (MJD) models, I will show how Levy processes arise naturally to model the dynamics of stocks and will focus on their characteristic function in connection with Fourier Transforms. Fast Fourier Transform methods are then discussed to price options as presented by P. Carr (1999). I then address convergence issues and will present the results obtained for BS, MJD and Variance Gamma.

An introduction to Fourier Transform and Option Pricing

October 14Duration: Investments and (Partial) Derivatives - Joseph Boor, FSUThis presentation will discuss the use of duration analysis to control the risks of changing interest rates on financial intermediaries such as insurance companies and pension funds. Those entities, by their nature, tend to have a substantial number of financial obligations that must be paid in the future (liabilities) and a substantial amount of investments, often in bonds('assets') that are intended to come due from others with enough payout to 'fund' the liabilities. The concept of investment duration was invented (by Frederick Macaulay) as a methodology to help protect the 'surplus' or 'net worth' of the intermediary, which is the excess of the assets over the liabilities. To do so, certain assets are designated to fund the liabilities, the remaining assets are segregated as the surplus, and duration and present value matching between the liabilities and the assets used to fund them is used to ensure minimal impacts of interest rate changes on the difference ('portfolio value') between the liabilities and the assets used to fund them, ensuring stability (up to the risk assumed in investing the surplus) of the surplus should interest rates change.

To presentation will begin with examples of how changing interest rates can affect the present or market value of bonds, and illustrate how a portfolio of assets and liabilities that are not well matched may suffer swings in value as interest rates change. It will then focus on so-called 'duration matching', first by absolute matching of assets and liabilities, then presenting the mathematics of investment duration as a consequence of differentiating present values of portfolios by the interest rate used to value them. So called 'full immunization' using the second derivative will be discussed as well. And the importance of equality of the present values of the assets and liabilities will be discussed. An example of single/double assets duration matching will be presented. Next, an example of the so-called 'liquidity preference', it's rationale and the normal shape of the 'yield curve' of interest rates of various investment point durations will be presented. And a discussion of how insurance companies manage the 'duration gap' and why will be presented in light of the yield curve. Lastly, a brief discussion of the limitations of duration matching in the real-world environment where each asset maturity features a different interest rate will be presented.

As an alternative more suited to the real world interest rate environment, duration mattching/immunization with respect to the loadings of the three factors presented by Litterman and Scheinkman will be presented. The calculations for the responsiveness or duration of a portfolio to the three Litterman/Scheinkman factors will be derived, as well as the second derivative quantities required for 'full immmunization' with respect to the Litterman/Scheinkman factors. A spreadsheet example showing how Litterman/Scheinkman duration matching may be coupled with a target strategy to achieve asset/liability 'alpha'. Lastly, potential roles of interest rate models in achieving alpha, and the importance of the broad assumprtions of the model used will be presented.

October 21An Adaptive Spectral Element Method to Price American Options - Matthew Willyard, FSUWe price American options using a new adaptive spectral element method. We develop an adjoint-based global error estimator that determines where (de)refinement is needed. Then we use a work estimator to decide between h and p-(de)refinement. The result is an approximation with an error within prescribed tolerances solved on meshes that use far fewer nodes than the uniform mesh required for the same error level.

October 28Special Seminar - Dr. Steve Perfect, NextEra Energy.

November 4No Seminar

November 11Veterans' Day Holiday

November 18Pricing Digital Options with High Resolution Methods - Ahmed Derar Islim, FSUATE paper

December 2Catastrophes and the Demand for Life Insurance - James M. Carson, FSUPrior research suggests that the occurrence of a catastrophe may lead to increases in risk mitigation, risk perception, and the demand for insurance. Given the extensive damage inflicted by major natural disasters, such a phenomenon is intuitive for property risk. However, the literature includes theory and evidence that suggest a broader behavioral perspective, and we therefore examine the possible link between catastrophes and subsequent demand for insurance against mortality risk. Based on U.S. state-level data for the period 1997 through 2008, we provide evidence of a significant positive relationship between catastrophes and life insurance demand. The finding holds both for states directly affected by the event and for neighboring states. In addition, evidence suggests that post-catastrophe life insurance demand is sensitive to the size of the catastrophe.

Catastrophes and the Demand for Life Insurance