A Wavelet-Based Analysis of Commodity Futures Markets

Power, Gabriel. 2007. A Wavelet-Based Analysis of Commodity Futures Markets. Doctoral Dissertation, Cornell University.

The time horizon of decision-making is an essential dimension of economic problems but is difficult to explicitly define. In this thesis, we use time series analysis augmented by wavelet transform methods to precisely identify distinct time horizons in economic data and measure their explanatory power. This enables us to address three timely and persistent questions in the literature on commodity derivatives markets are addressed. First, are findings of long memory (fractional integration) in commodity futures price volatility spurious, following Granger?s conjecture? Yes, only two out of eleven commodities are characterized by true long memory and certain stochastic break models (e.g. Markov-switching) are found to be more plausible. Second, do large Index Traders such as commodity pools and pension funds increase futures price volatility through a large volume of trading activity? This appears to be true only for non-storable commodity contracts. Third, can we improve the accuracy of term structure models of futures prices by (i) including more state variables to better capture maturity and inventory effects, and (ii) filtering out what appears to be noise at the shortest time horizons? The results suggest that (i) three state variables is an optimal choice and (ii) estimates using filtered data are not improved and the noise may be economically meaningful.

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Mathematical Models For Swing Options And Subprime Mortgage Derivatives

Diener, Nicolas. 2009. Mathematical Models For Swing Options And Subprime Mortgage Derivatives. Doctoral Dissertation, Cornell University.

The deregulation of the energy market and the recent soaring (and possible bubble) of commodity prices motivates the first part of the thesis. We analyze a certain kind of contract in the commodity market known as swing or take-or-pay options. These contracts are American type options where the holder has multiple exercise rights. The goal is to find the optimal consumption process for the underlying commodity. We present a pricing methodology using the theory of reflected backward stochastic differential equations and the theory of Snell envelopes. Once the model is constructed, one can use numerical techniques to solve the pricing problem and compute a replicating strategy using forward contracts. The recent burst of the real estate bubble has drawn a lot of attention to the subprime derivatives market. Existing models have proven inadequate due to their inability to account for the complexity of mortgage derivatives. Chapter 3 provides an analytical framework for understanding the mortgage market. In Chapter 4, we give a condition on the underlying securities that allows us to directly compute the loss distribution term structure of the portfolio. Then, we build a tractable model for pricing options on large credit portfolios such as Collateralized Debt Obligations of subprime Asset Backed Securities / Home Equity Loans.

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Factor Models For Call Price Surface Without Static Arbitrage

Zhu, Fan. 2012. Factor Models For Call Price Surface Without Static Arbitrage. Doctoral Dissertation, Cornell University.

Although stochastic volatility models and local volatility model are very popular among the market practitioner for exotic option pricing and hedging, they have several critical defects both in theory and practice. We develop a new methodology for equity exotic option pricing and hedging within the market based approach framework. We build stochastic factor models for the whole surface of European call option prices directly from the market data, and then use this model to price exotic options, which is not liquidly traded. The factor models are built based on Karhunen-Loeve decomposition, which can be viewed as an infinite dimensional PCA. We develop the mathematical framework of centered and uncentered versions of the Karhunen-Loeve decomposition and study how to incorporate critical shape constraints. The shape constraints are important because no static arbitrage conditions should be satisfied by our factor models. We discuss this methodology theoretically and investigate it by applying to the simulated data.

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Investigation of Interest Rate Derivatives by Quantum Finance

Liang, Cui. 2008. Investigation of Interest Rate Derivatives by Quantum Finance. Doctoral Dissertation, NUS.

Interest rate derivatives are the largest derivatives market in the world. In order to price different interest rate derivatives, one needs to model the underlying forward interest rate. Quantum finance developed by Baaquie is a framework to model non-trivial correlations between forward interest rates with different maturities as a parsimonious alternative to the existing interest rate theories in finance, in particular to the HJM-model. Base on the Quantum Finance framework, we empirically studied the Cap and Floor pricing, unlike Black's formula, the Quantum Finance formula generates the market price to an accuracy better than 90%.Also for swaption, the perturbation expansion formula generates the prices to an accuracy of about 95% and matches all the trends of the market. We also give a efficient algorithm for pricing American option on interest rate based on lattice field theory model.

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Exotic Interest Rate Options in Quantum Finance

Pan, Tang. 2010. Exotic Interest Rate Options in Quantum Finance. Doctoral Dissertation, NUS.

A major subject matter of this thesis is focused on studying the generalized forward interest rate model and the Libor Market Model in Quantum Finance. Compared to the stochastic interest rate models, the imperfectly correlated interest rates are modeling as a Gaussian field. The feature of the Gaussian field is that it contains much more information than the one-dimensional stochastic processes, which drive the entire evolution of interest rates in traditional financial theory. The simulation algorithm for modeling interest rates is extensively studied. Due to the complex structure of interest rate instruments, the approximate price only can be derived based on the perturbation expansion for small value of volatility. The comparison between simulation results and analytical formula is studied for many instruments and shows the flexible and potential of simulation method in pricing interest rate derivatives. In particular, it is shown that the simulation method provides a powerful tool in studying any kind of interest rate instruments without limitation. Another part of this thesis is studying the Constant Elasticity of Variance (CEV) process. A recursion equation of CEV process is developed and used to calibrate the value of beta, which is the key term in CEV model. The value of beta for market observed Equity Default Swaps (EDS) spreads is obtained and agrees with the recent studies. However, the results for Credit Default Swaps (CDS) show that the market observed CDS spreads have no sensitivity to the implied volatility, which cannot be explained by CEV process. It is suggested that the EDS spreads with low barriers are more attractive to the market compared to CDS spreads. In the third part, an unequal time Gaussian model is developed to calibrate the stock market data. The nontrivial Lagrangian is defined and the unequal time propagator is studied for fitting the correlation of different stocks on different time. Compared to modern portfolio theory, Gaussian model is more powerful in describing the behavior of unequal time correlation. Based on the nontrivial Lagrangian, Gaussian model is generally applicable to other liquid markets which have strong unequal time correlation.

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