Machine learning Vasicek model calibration with Gaussian processes

In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.

Credit risk & forward price models

Doutoramento em Gestão

Skewness risk and bond prices

Statistical evidence is reported that even outside disaster periods, agents face negative consumption skewness, as well as positive inflation skewness. Quantitative implications of skewness risk for nominal loan contracts in a pure exchange economy are derived. Key modeling assumptions are Epstein-Zin preferences for traders and asymmetric distributions for consumption and inflation innovations. The model is solved using a third-order perturbation and estimated by the simulated method of moments. Results show that skewness risk accounts for 6 to 7 percent of the risk premia depending on the bond maturity.

$80,000,000 State of Illinois general obligation college savings bonds : series of October 2002 (zero coupon bonds)

"Due: August 1, as shown below."

$101,855,028.75 State of Illinois general obligation college savings bonds : series of October 2000 (zero coupon bonds)

"New issue."

$80,000,000 State of Illinois general obligation college savings bonds : series of October 2000 (zero coupon bonds).

"Due: August 1, as shown below."

Investigation of Pr valence and relationship between bond covalency and T-c in Y1-xPrxBa2Cu3O7 (x = 0-1)

The valence of Pr and relationship between bond covalency and T-c in Y1-xPrxBa2Cu3O7 (x = 0-1) have been studied using complex chemical bond theory. The results indicate that the depression of superconductivity in Y1-xPrxBa2Cu3O7 can be reasonably explained by bond covalency difference for the bonds between CuO2 plane and CuO chain. T-c decreases with the decreasing of bond covalency difference and reaches zero when bond covalency difference is zero (or bond covalency in CuO2 exceeds that in CuO chain) at Pr concentration 0.55 and valence +3.30. These are in good agreement with the experiments and meanwhile suggest that the valence of Pr is + 3.30 in Y1-xPrxBa2Cu3O7. The results also indicate that for Pr valence less than +3.15, superconductivity always exists for whatever Pr concentration, whereas for Pr with a valence of +4.0, superconductivity disappears as soon as Pr concentration exceeds 0.19. This supports with the viewpoint that higher valence Pr will contribute more electrons to CuO2 plane, filling the mobile holes responsible for conduction. For PrBa2Cu3O7 with no Ba-site Pr, our calculation suggests that it will be a superconductor if the average valence of Pr is less than +3.15. (C) 1998 Published by Elsevier Science B.V. All rights reserved.

Three essays on the term structure of interest rates

A PhD Dissertation, presented as part of the requirements for the Degree of Doctor of Philosophy from the NOVA - School of Business and Economics

Data uncertainty in real estate forecasting

The rapid expansion of the TMT sector in the late 1990s and more recent growing regulatory and corporate focus on business continuity and security have raised the profile of data centres. Data centres offer a unique blend of occupational, physical and technological characteristics compared to conventional real estate assets. Limited trading and heterogeneity of data centres also causes higher levels of appraisal uncertainty. In practice, the application of conventional discounted cash flow approaches requires information about a wide range of inputs that is difficult to derive from limited market signals or estimate analytically. This paper outlines an approach that uses pricing signals from similar traded cash flows is proposed. Based upon ‘the law of one price’, the method draws upon the premise that two identical future cash flows must have the same value now. Given the difficulties of estimating exit values, an alternative is that the expected cash flows of data centre are analysed over the life cycle of the building, with corporate bond yields used to provide a proxy for the appropriate discount rates for lease income. Since liabilities are quite diverse, a number of proxies are suggested as discount and capitalisation rates including indexed-linked, fixed interest and zero-coupon bonds. Although there are rarely assets that have identical cash flows and some approximation is necessary, the level of appraiser subjectivity is dramatically reduced.

The appraisal of data centres: deconstructing the cash flow

This paper analyses the appraisal of a specialized form of real estate - data centres - that has a unique blend of locational, physical and technological characteristics that differentiate it from conventional real estate assets. Market immaturity, limited trading and a lack of pricing signals enhance levels of appraisal uncertainty and disagreement relative to conventional real estate assets. Given the problems of applying standard discounted cash flow, an approach to appraisal is proposed that uses pricing signals from traded cash flows that are similar to the cash flows generated from data centres. Based upon ‘the law of one price’, it is assumed that two assets that are expected to generate identical cash flows in the future must have the same value now. It is suggested that the expected cash flow of assets should be analysed over the life cycle of the building. Corporate bond yields are used to provide a proxy for the appropriate discount rates for lease income. Since liabilities are quite diverse, a number of proxies are suggested as discount and capitalisation rates including indexed-linked, fixed interest and zero-coupon bonds.

Testing term structure estimation methods:evidence from the UK STRIPs market

Prices and yields of UK government zero-coupon bonds are used to test alternative yield curve estimation models. Zero-coupon bonds permit a more pure comparison, as the models are providing only the interpolation service and also not making estimation feasible. It is found that better yield curves estimates are obtained by fitting to the yield curve directly rather than fitting first to the discount function. A simple procedure to set the smoothness of the fitted curves is developed, and a positive relationship between oversmoothness and the fitting error is identified. A cubic spline function fitted directly to the yield curve provides the best overall balance of fitting error and smoothness, both along the yield curve and within local maturity regions.

Principles of investments

"Emphasises asset allocation while presenting the practical applications of investment theory. The authors concentrate on the intuition and insights that will be useful to students throughout their careers as new ideas and challenges emerge from the financial marketplace. It provides a good foundation to understand the basic types of securities and financial markets as well as how trading in those markets is conducted. The Portfolio Management section is discussed towards the end of the course and supported by a web-based portfolio simulation with a hypothetical $100,000 brokerage account to buy and sell stocks and mutual funds. Students get a chance to use real data found in the Wall Street Survivor simulation in conjunction with the chapters on investments. This site is powered by StockTrak, the leading provider of investment simulation services to the academic community. Principles of Investments includes increased attention to changes in market structure and trading technology. The theory is supported by a wide range of exercises, worksheets and problems."--publisher website Contents: Investments: background and issues -- Asset classes and financial markets -- Securities markets -- Managed funds and investment management -- Risk and return: past and prologue -- Efficient diversification -- Capital asset pricing and arbitrage pricing theory -- The efficient market hypothesis -- Bond prices and yields -- Managing bond portfolios -- Equity valuation -- Macroeconomic and industry analysis -- Financial statement analysis -- Investors and the investment process -- Hedge funds -- Portfolio performance evaluation.

Financial Markets, Institutions and Money [3rd ed.]

"The financial system is a key influencer of the health and efficiency of an economy. The role of the financial system is to gather money from people and businesses that currently have more money than they need and transfer it to those that can use it for either business or consumer expenditures. This flow of funds through financial markets and institutions in the Australian economy is huge (in the billions of dollars), affecting business profits, the rate of inflation, interest rates and the production of goods and services. In general, the larger the flow of funds and the more efficient the financial system, the greater the economic output and welfare in the economy. It is not possible to have a modern, complex economy such as that in Australia, without an efficient and sound financial system. The global financial crisis (GFC) of late 2007–09 (and the ensuing European debt crisis), where the global financial market was on the brink of collapse with only significant government intervention stopping a catastrophic global failure of the market, illustrated the importance of the financial system. Financial Markets, Institutions and Money 3rd edition introduces students to the financial system, its operations, and participants. The text offers a fresh, succinct analysis of the financial markets and discusses how the many participants in the financial system interrelate. This includes coverage of regulators, regulations and the role of the Reserve Bank of Australia, that ensure the system’s smooth running, which is essential to a modern economy. The text has been significantly revised to take into account changes in the financial world."---publisher website Table of Contents 1. The financial system - an overview 2. The Monetary Authorities 3. The Reserve Bank of Australia and interest rates 4. The level of interest rates 5. Mathematics of finance 6. Bond Prices and interest rate risk 7. The Structure of Interest Rates 8. Money Markets 9. Bond Markets 10. Equity Markets

Pricing Defaultable Bonds in a Markov Modulated Market

We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in a Markov modulated market. Since the market is incomplete, we use the method of quadratic hedging and minimal martingale measure to derive locally risk minimizing derivative prices, hedging strategies and the corresponding residual risks. The price of defaultable bonds are obtained as solutions to a system of PDEs with weak coupling subject to appropriate terminal and boundary conditions. We solve the system of PDEs numerically and carry out a numerical investigation for the defaultable bond prices. We compare their credit spreads with some of the existing models. We observe higher spreads in the Markov modulated market. We show how business cycles can be easily incorporated in the proposed framework. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low risk-free interest rate, high payout rate and high volatility.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.