The price of power: The valuation of power and weather derivatives

Pricing contingent claims on power presents numerous challenges due to (1) the unique behavior of power prices, and (2) time-dependent variations in prices. We propose and implement a model in which the spot price of power is a function of two state variables: demand (load) and fuel price. In this model, any power derivative price must satisfy a PDE with boundary conditions that reflect capacity limits and the non-linear relation between load and the spot price of power. Moreover, since power is non-storable and demand is not a traded asset, the power derivative price embeds a market price of risk. Using inverse problem techniques and power forward prices from the PJM market, we solve for this market price of risk function. During 1999–2001, the upward bias in the forward price was as large as $50/MWh for some days in July. By 2005, the largest estimated upward bias had fallen to $19/MWh. These large biases are plausibly due to the extreme right skewness of power prices; this induces left skewness in the payoff to short forward positions, and a large risk premium is required to induce traders to sell power forwards. This risk premium suggests that the power market is not fully integrated with the broader financial markets.     

Disagreement and asset prices

How do differences of opinion affect asset prices? Do investors earn a risk premium when disagreement arises in the market? Despite their fundamental importance, these questions are among the most controversial issues in finance. In this paper, we use a novel data set that allows us to directly measure the level of disagreement among Wall Street mortgage dealers about prepayment speeds. We examine how disagreement evolves over time and study its effects on expected returns, return volatility, and trading volume in the mortgage-backed security market. We find that increased disagreement is associated with higher expected returns, higher return volatility, and larger trading volume. These results imply that there is a positive risk premium for disagreement in asset prices. We also show that volatility in and of itself does not lead to higher trading volume. Instead, only when disagreement arises in the market is higher uncertainty associated with more trading. Finally, we are able to distinguish empirically between two competing hypotheses regarding how information in markets gets incorporated into asset prices. We find that sophisticated investors appear to update their beliefs through a rational expectations mechanism when disagreement arises.     

Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium

In this paper we provide a framework that explains how the market risk premium, defined as the difference between forward prices and spot forecasts, depends on the risk preferences of market players and the interaction between buyers and sellers. In commodities markets this premium is an important indicator of the behavior of buyers and sellers and their views on the market spanning between short-term and long-term horizons. We show that under certain assumptions it is possible to derive explicit solutions that link levels of risk aversion and market power with market prices of risk and the market risk premium. We apply our model to the German electricity market and show that the market risk premium exhibits a term structure which can be explained by the combination of two factors. Firstly, the levels of risk aversion of buyers and sellers, and secondly, how the market power of producers, relative to that of buyers, affects forward prices with different delivery periods.     

The Forward Premium in the Nord Pool Power Market

This article investigates the forward premium of futures contracts in the Nordic power market for the time period from January 2004 to December 2013. We find that futures prices are biased predictors of the subsequent spot prices and that there is a significant forward premium in the Nord Pool market, particularly during the winter and autumn. We analyze the impact from several factors on the forward premium. The spot price, and the deviation of water inflow from its usual level, positively affect the forward premium. The variance of the spot price also has a positive effect on the forward premium, but only for the contract closest to delivery.     

Seasonality and the valuation of commodity options

Price movements in many commodity markets exhibit significant seasonal patterns. However, given an observed futures price, a deterministic seasonal component at the price level is not relevant for the pricing of commodity options. In contrast, this is not true for the seasonal pattern observed in the volatility of the commodity price. Analyzing an extensive sample of soybean, corn, heating oil and natural gas options, we find that seasonality in volatility is an important aspect to consider when valuing these contracts. The inclusion of an appropriate seasonality adjustment significantly reduces pricing errors in these markets and yields more improvement in valuation accuracy than increasing the number of stochastic factors.     

The dynamics of quote adjustments

Liquidity providers on the NYSE make faster quote adjustments towards equilibrium spreads and depths than they do on NASDAQ. Liquidity providers in both markets make faster spread and depth adjustments for stocks with more frequent trading, greater return volatility, higher prices, smaller market capitalizations, and smaller trade sizes. We find that stocks with greater information-based trading and in more competitive trading environments exhibit faster quote adjustments. The speed of quote adjustment is faster after decimalization in both markets. These results are robust and not driven by differences in stock attributes between the two markets or time periods. Overall, our results indicate that stock attributes, market structure, and tick size exert a significant impact on the speed of quote adjustment.     

Locals, foreigners, and multi-market trading of equities: Intraday evidence from Thailand

We study stock market orders and trades in a developing country, Thailand, where foreign ownership limits partially segment local and foreign investors into two distinct markets. Some foreigners forgo voting rights and distributions to trade on the “local board”, while some locals forgo such benefits and pay a price premium to trade on the “foreign board”. Regardless of nationality, these cross-market traders typically submit orders when liquidity is high, fill orders at relatively beneficial prices, exploit patterns in stock prices across markets, display profitable holding-period returns, and enhance price discovery. This suggests that skilled, informed trading that affects market quality does not depend on trader nationality.     

Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets

Spot power prices are volatile and since electricity cannot be economically stored, familiar arbitrage-based methods are not applicable for pricing power derivative contracts. This paper presents an equilibrium model implying that the forward power price is a downward biased predictor of the future spot price if expected power demand is low and demand risk is moderate. However, the equilibrium forward premium increases when either expected demand or demand variance is high, because of positive skewness in the spot power price distribution. Preliminary empirical evidence indicates that the premium in forward power prices is greatest during the summer months.     

Footprints in the market: Hedge funds and the carry trade

This paper uses a new database provided by the Commodity and Futures Trading Commissions to examine the price impact of hedge fund carry trades in “hot” and “cold” markets. We find that hedge funds significantly increase their carry trade positions during hot markets (periods with very high currency returns). Consistent with currency overpricing, positions in hot markets are followed by exchange rate reversals. Optimism in the stock market seems to have a spillover effect on hedge fund speculation in the currency market: controlling for the variance risk premium fully accounts for the reversal effect. Overall, our results add to a growing body of empirical evidence that institutional demand can move asset prices.     

Preference heterogeneity and asset prices: An exact solution

We introduce a general equilibrium model of a multi-agent, pure-exchange economy and find a set of conditions that enable us to obtain explicit closed-form solutions to the equilibrium interest rate, stock price, risk premium and stock market volatility when investors have heterogenous risk aversions. Because the market is dynamically complete, full risk sharing obtains and a representative agent can be constructed, though the risk aversion of this agent fluctuates over time with the state of the economy, as the relative wealth distribution of the individual investors changes. We show that preference heterogeneity can cause asset prices to be significantly more volatile than the underlying dividends and that it can lead to leverage-like effects in volatility, in the sense that volatility increases after stock-market declines.     

Limits to arbitrage and hedging: Evidence from commodity markets

We build an equilibrium model of commodity markets in which speculators are capital constrained, and commodity producers have hedging demands for commodity futures. Increases in producers' hedging demand or speculators' capital constraints increase hedging costs via price-pressure on futures. These in turn affect producers' equilibrium hedging and supply decision inducing a link between a financial friction in the futures market and the commodity spot prices. Consistent with the model, measures of producers' propensity to hedge forecasts futures returns and spot prices in oil and gas market data from 1979 to 2010. The component of the commodity futures risk premium associated with producer hedging demand rises when speculative activity reduces. We conclude that limits to financial arbitrage generate limits to hedging by producers, and affect equilibrium commodity supply and prices.     

Understanding Housing Market Volatility

The Campbell–Shiller present value formula implies a factor structure for the price–rent ratio of housing market. Using a dynamic factor model, we decompose the price–rent ratios of 23 major housing markets into a national factor and independent local factors, and we link these factors to the economic fundamentals of the housing markets. We find that a large fraction of housing market volatility is local and that the national factor has become more important than local factors in driving housing market volatility since 1999, consistent with the findings in Del Negro and Otrok (2007). The local volatilities mostly are due to time variations of idiosyncratic housing market risk premia, not local growth. At the aggregate level, the growth and interest rate factors jointly account for less than half of the total variation in the price–rent ratio. The rest is due to the aggregate housing market risk premium and a pricing error. We find evidence that the pricing error is related to money illusion, especially at the onset of the recent housing market bubble. The rapid rise in housing prices prior to the 2008 financial crisis was accompanied by both a large increase in the pricing error and a large decrease in the housing market risk premium.     

Does futures exhibit maturity effect? New evidence from an extensive set of US and foreign futures contracts

In a seminal article, Samuelson (1965) [Samuelson, P. A. (1965), “Proof that properly anticipated prices fluctuate randomly,” Industrial Management Review 6, 41-49.] proposes the maturity effect that the volatility of futures prices should increase as futures contract approaches maturity. This study provides new evidence on the maturity effect by examining a more extensive set of futures contracts than previous studies and analyzing each contract separately. Using 6805 futures contracts drawn from 61 commodities, including some data from non-US markets, we find that the maturity effect is absent in the majority of contracts. In addition, the maturity effect tends to be stronger in agricultural and energy commodities than in financial futures. We also examine the hypothesis in Bessembinder et al. (1996) [Bessembinder, H., J. F. Coughenour, P. J. Seguin, & M. M. Smoller (1996), “Is there a term structure of futures volatilities? Reevaluating the Samuelson hypothesis,” Journal of Derivatives 4, 45-58.], which states that negative covariance between the spot price and net carry cost causes the maturity effect in futures. Our results provide very weak evidence in favor of this hypothesis.     

Do the Forward Sales of Real Estate Stabilize Spot Prices?

We examine the effect of forward sale (pre-sale) activities on the volatility of spot prices in the real estate market. The abundance of pre-sales data and major changes in regulatory control on the pre-sale market during the 90's in Hong Kong allow us to undertake empirical tests using Hong Kong's real estate data. Our results show that the volatility of spot prices increased significantly after forward sales were severely dampened by regulatory control measures introduced in 1994, but decreased again when the measures were partly relaxed in 1998. The results contribute to the long lasting debate on whether the introduction of a futures market reduces the volatility of spot prices. Previous studies were mainly conducted in markets with low transaction costs, notably financial markets. By utilizing the unique regulatory changes in the pre-sale market of Hong Kong, we are able to conduct an experiment on the conditional volatility of spot prices in a high information-cost environment, thereby shedding light on the important role of forward housing contracts in providing price expectation information for spot trading.     

Optimal Portfolio Choices, House Risk Hedging and the Pricing of Forward House Transactions

This paper develops a utility indifference model for evaluating various prices associated with forward transactions in the housing market, based on the equivalent principle of expected wealth utility derived from the forward and spot real estate markets. Our model results show that forward transactions in the housing market are probably not due to house sellers?? and buyers?? heterogeneity, but to their demand for hedging against house price risk. When the imperfections of real estate markets and the risk preferences of market participants are taken into consideration, we are able to show that the idiosyncratic risk premium, which mainly depends on the participants?? risk preferences and the correlation between the traded asset and the real estate, is a remarkable determinant of house sellers?? and buyers?? forward reservation prices. In addition, we also find that the market clearing forward price usually will not converge toward the expected risk-neutral forward price. The sellers?? or buyers?? risk aversion degrees and market powers are also identified to play crucial roles in determining the clearing forward price.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.     

Is market fragmentation harming market quality?

We examine how fragmentation is affecting market quality in US equity markets. We use newly available trade reporting facilities (TRFs) data to measure fragmentation, and we use a variety of empirical approaches to compare execution quality and efficiency of stocks with more and less fragmented trading. We find that fragmentation affects all stocks; more fragmented stocks have lower transactions costs and faster execution speeds; and fragmentation is associated with higher short-term volatility but greater market efficiency, in that prices are closer to being a random walk. Our results that fragmentation does not appear to harm market quality are consistent with US markets being a single virtual market with multiple points of entry.     

From boom ‘til bust: How loss aversion affects asset prices

This article studies the impact of heterogeneous loss averse investors on asset prices. In very good states loss averse investors become gradually less risk averse as wealth rises above their reference point, pushing up equity prices. When wealth drops below the reference point the investors become risk seeking and demand for stocks increases drastically, eventually leading to a forced sell-off and stock market bust in bad states. Heterogeneity in reference points and initial wealth of the loss averse investors does not change the salient features of the equilibrium price process, such as a relatively high equity premium, high volatility and counter-cyclical changes in the equity premium.     

Beyond Basis Basics: Liquidity Demand and Deviations from the Law of One Price

Deviations from the law of one price between futures and spot prices—the futures-cash basis—capture information about liquidity demand for equity market exposure in global markets. We show that the basis comoves with dealer and investor futures positions, is contemporaneously positively correlated with futures and spot market returns, and negatively predicts futures and spot returns. These findings are consistent with the futures-cash basis reflecting liquidity demand that is common to futures and cash equity markets. We find persistent supply-demand imbalances for equity index exposure reflected in the basis, giving rise to an annual premium of 5% to 6%.     

Locals,foreigners, and multi-market trading of equities: Intraday evidence from Thailand

We study stock market orders and trades in a developing country, Thailand, where foreign ownership limits partially segment local and foreign investors into two distinct markets. Some foreigners forgo voting rights and distributions to trade on the “local board”, while some locals forgo such benefits and pay a price premium to trade on the “foreign board”. Regardless of nationality, these cross-market traders typically submit orders when liquidity is high, fill orders at relatively beneficial prices, exploit patterns in stock prices across markets, display profitable holding-period returns, and enhance price discovery. This suggests that skilled, informed trading that affects market quality does not depend on trader nationality.