A Fair Pricing Approach to Weather Derivatives

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative price processes are martingales. No measure transformation is needed for the proposed fair pricing. For weather derivative payoffs that are independent of the value of the growth optimal portfolio, it is shown that the classical actuarial pricing methodology is a particular case of the fair pricing concept. A discrete time model is constructed to approximate historical weather characteristics. The fair prices of some particular weather derivatives are derived using historical and Gaussian residuals. The question of weather risk as diversifiable risk is also discussed. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: C16, G10, G13     

Diversified Portfolios with Jumps in a Benchmark Framework

This paper considers diversified portfolios in a sequence of jump diffusion market models. Conditions for the approximation of the growth optimal portfolio (GOP) by diversified portfolios are provided. Under realistic assumptions, it is shown that diversified portfolios approximate the GOP without requiring any major model specifications. This provides a basis for systematic use of diversified stock indices as proxies for the GOP in derivative pricing, risk management and portfolio optimization. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

A Benchmark Approach to Portfolio Optimization under Partial Information

This paper proposes a filtering methodology for portfolio optimization when some factors of the underlying model are only partially observed. The level of information is given by the observed quantities that are here supposed to be the primary securities and empirical log-price covariations. For a given level of information we determine the growth optimal portfolio, identify locally optimal portfolios that are located on a corresponding Markowitz efficient frontier and present an approach for expected utility maximization. We also present an expected utility indifference pricing approach under partial information for the pricing of nonreplicable contracts. This results in a real world pricing formula under partial information that turns out to be independent of the subjective utility of the investor and for which an equivalent risk neutral probability measure need not exist.      

A Two-Factor Model for Low Interest Rate Regimes

This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is neither possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

Interest Rate Risk Rewards in Stock Returns of Financial Corporations: Evidence from Germany

The interest rate sensitivity of stock returns of financial and non-financial corporations is a well-known phenomenon. However, only little is known about the part of total stock returns that is attributable to the compensation an investor receives for being exposed to interest rate risk when investing in equity securities. We pursue here a benchmark portfolio approach, constructing benchmark portfolios having the same interest rate risk exposure as a particular stock. By studying the time series of returns of these asset-specific benchmarks, we find: i) Regardless of the industry considered, the interest rate risk benchmarks of German corporations have mostly earned a significantly positive reward. ii) Returns of interest rate risk benchmarks of financial institutions exceeded significantly those of non-financial corporations. iii) An investor willing to bear nothing but the average interest rate risk of German financial institutions would have earned a mean return of about or even exceeding 70% of the corresponding total stock returns. iv) Returns of the interest rate risk benchmarks of the German insurance sector were significantly higher than those of German banks, which seems to contradict conventional market wisdom that insurances hedge interest rate risks.     

Understanding the Implied Volatility Surface for Options on a Diversified Index

This paper describes a two-factor model for a diversified index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market activity time where the discounted growth optimal portfolio is expressed as a time transformed squared Bessel process of dimension four. It turns out that for this index model an equivalent risk neutral martingale measure does not exist because the corresponding Radon-Nikodym derivative process is a strict local martingale. However, a consistent pricing and hedging framework is established by using the benchmark approach. The proposed model, which includes a random initial condition for market activity, generates implied volatility surfaces for European call and put options that are typically observed in real markets. The paper also examines the price differences of binary options for the proposed model and their Black-Scholes counterparts. Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

Volatility Spillover in Regional Emerging Stock Markets: A Structural Time-Series Approach

Volatility spillovers among the stock markets of Bahrain, Kuwait, and Saudi Arabia are investigated using the concept of stochastic volatility and structural time-series modeling. The results reveal volatility spillovers, in which the Kuwait market plays the major role. It is also found that volatility in one market cannot be explained fully in terms of volatility in the other two markets, but that, out of the three markets, the Kuwait market seems to be the most influential. Some explanations are put forward for why this is the case.     

A note on a semiparametric approach to estimating financing constraints in firms

In this paper, we present a novel approach to modeling financing constraints of firms. Specifically, we adopt an approach in which firm-level investment is a nonparametric function of some relevant firm characteristics, cash flow in particular. This enables us to generate firm-year specific measures of cash flow sensitivity of investment. We are therefore able to draw conclusions about financing constraints of individual firms as well as cohorts of firms without having to split our sample on an ad hoc basis. This is a significant improvement over the stylized approach that is based on comparison of point estimates of cash flow sensitivity of investment of the average firm of ad hoc sub-samples of firms. We use firm-level data from India to highlight the advantages of our approach. Our results suggest that the estimates generated by this approach are meaningful from an economic point of view and are consistent with the literature.     

A minimum variance benchmark to measure the performance of pension funds in Mexico

We propose the use of the minimum variance portfolio as weighting method in a strategy benchmark for pension funds performance in Mexico. By performing three discrete event simulations with daily data from January 2002 to May 2013, we test this benchmark's weighting method against the Max Sharpe ratio one and a linear combination of both benchmarks (minimum variance and Max Sharpe). With the Sharpe ratio, the Jensen's alpha significance test and the Huberman and Kandel’ (1987) spanning test, we found that the three benchmarks have a statistically equal performance. By using Bailey's (1992) risk exposure, market representativeness and turnover benchmark quality criteria, we found that the min variance is preferable for the publicly traded Mexican defined contribution pension funds.