Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for the pricing of interest rate derivatives, using panel data on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both models we analyze how well they price caplets and swaptions that were not used for calibration. We show that the Libor Market Model in general leads to better prediction of derivative prices that were not used for calibration than the Swap Market Model. Also, we find that Market Models with a declining volatility function give much better pricing results than a specification with a constant volatility function. Finally, we find that models that are chosen to exactly match certain derivative prices are overfitted; more parsimonious models lead to better predictions for derivative prices that were not used for calibration.     

A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk.As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. The q-optimal pricing measure is related to the marginal utility indifference price of an agent with constant relative risk aversion. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same.As a concrete example, we specialize to a variant of the Hull-White or Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter q. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying q.JEL Classification: D52, G13     

A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks

We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network-pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with the no-arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis function networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1991.     

Asset pricing under information with stochastic volatility

Based on a general specification of the asset specific pricing kernel, we develop a pricing model using an information process with stochastic volatility. We derive analytical asset and option pricing formulas. The asset prices in this rational expectations model exhibit crash-like, strong downward movements. The resulting option pricing formula is consistent with the strong negative skewness and high levels of kurtosis observed in empirical studies. Furthermore, we determine credit spreads in a simple structural model.      

Dual transfer pricing with internal and external trade

This paper examines a transfer pricing problem between two divisions of a decentralized firm. The selling division is privately informed about its own costs and produces a good that is sold both externally in an intermediate market and internally within the firm. Unlike most previous work, we focus on dual transfer pricing systems that allow the selling division to be credited for an amount that differs from the amount charged to the buying division. We identify conditions under which efficient decentralized trade and external price setting incentives can be provided with a properly chosen set of dual transfer prices that do not rely on direct communication. Instead, the optimal dual transfer prices will depend only on public information about the market price charged by the upstream division in the external market, which indirectly communicates information about production costs to the downstream division. For a variety of well-known demand functions, the optimal transfer prices will be linear functions of the market price. Our main results hold when the upstream division faces multiple internal buyers or faces a binding capacity constraint.     

Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for thepricing of interest rate derivatives, using panel data on pricesof US caplets and swaptions. A Libor Market Model can directlybe calibrated to observed prices of caplets, whereas a SwapMarket Model is calibrated to a certain set of swaption prices.For both models we analyze how well they price caplets and swaptionsthat were not used for calibration. We show that the Libor MarketModel in general leads to better prediction of derivative pricesthat were not used for calibration than the Swap Market Model.Also, we find that Market Models with a declining volatilityfunction give much better pricing results than a specificationwith a constant volatility function. Finally, we find that modelsthat arechosen to exactly match certain derivative prices areoverfitted; more parsimonious models lead to better predictionsfor derivative prices that were not used for calibration. JELClassification: G12, G13, E43.     

Are structured products ‘fairly’ priced? An analysis of the German market for equity-linked instruments

Based on a unique data set, this paper examines the pricing of equity-linked structured products in the German market. The daily closing prices of a large variety of structured products are compared to theoretical values derived from the prices of options traded on the Eurex (European Exchange). For the majority of products, the study reveals large implicit premiums charged by the issuing banks in the primary market. A set of driving factors behind the issuers’ pricing policies is identified, for example, underlying and type of implicit derivative(s). For the secondary market, the product life cycle is found to be an important pricing parameter.     

Simulation-based pricing of convertible bonds

We propose and empirically investigate a pricing model for convertible bonds based on Monte Carlo simulation. The method uses parametric representations of the early exercise decisions and consists of two stages. Pricing convertible bonds with the proposed Monte Carlo approach allows us to better capture both the dynamics of the underlying state variables and the rich set of real-world convertible bond specifications. Furthermore, using the simulation model proposed, we present an empirical pricing study of the US market, using 32 convertible bonds and 69 months of daily market prices. Our results do not confirm the evidence of previous studies that market prices of convertible bonds are on average lower than prices generated by a theoretical model. Similarly, our study is not supportive of a strong positive relationship between moneyness and mean pricing error, as argued in the literature.     

Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices

Implicit in the prices of traded financial assets are Arrow–Debreu prices or, with continuous states, the state-price density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and we derive its asymptotic sampling theory. This estimator provides an arbitrage-free method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an asset-pricing perspective, for example, negative skewness and excess kurtosis for asset returns, and volatility "smiles" for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.     

How Much Do REITs Pay for Their IPOs?

Previous studies have documented the reversal in the initial returns of REIT IPOs from overpricing in the 1980s to underpricing in the 1990s. We find that the gross spreads of REIT IPOs decreased significantly in the 1990s. In particular, there is a bimodal clustering for gross spreads at 6.5 and 7.0%. Moreover, in the 1980s around 94% of REIT IPOs had integer offer prices, most of which were priced at either $10 or $20. However, the proportion of integer offer prices decreased to 64% in the 1990s. Higher gross spreads, overpricing, and high frequency of integer offer prices for REIT IPOs in the 1980s are consistent with the marketing hypothesis that in the 1980s REIT IPOs were mainly marketed to less-informed individual investors. Our results explain the dynamic process employed by underwriters in the setting of gross spreads and the pricing of REIT IPOs as a new financial product in response to various structural changes in REITs.     

Robust pricing and hedging under trading restrictions and the emergence of local martingale models

We pursue the robust approach to pricing and hedging in which no probability measure is fixed, but call or put options with different maturities and strikes can be traded initially at their market prices. We allow the inclusion of robust modelling assumptions by specifying a set of feasible paths on which (super)hedging arguments are required to work. In a discrete-time setup with no short selling, we characterise absence of arbitrage and show that if call options are traded, then the usual pricing–hedging duality is preserved. In contrast, if only put options are traded, a duality gap may appear. Embedding the results into a continuous-time framework, we show that the duality gap may be interpreted as a financial bubble and link it to strict local martingales. This provides an intrinsic justification of strict local martingales as models for financial bubbles arising from a combination of trading restrictions and current market prices.     

Derivative Pricing 60 Years before Black–Scholes: Evidence from the Johannesburg Stock Exchange

We obtain daily data for warrants traded on the Johannesburg Stock Exchange between 1909 and 1922, and for a broker's call option quotes on stocks from 1908 to 1911. We use this new data set to test how close derivative prices are to Black–Scholes (1973) prices and to compute profits for investors using a simple trading rule for call options. We examine whether investors exercised warrants optimally and how they reacted to extensions of the warrants' durations. We show that long before the development of the formal theory, investors had an intuitive grasp of the determinants of derivative pricing.     

Equilibrium asset pricing: with non-Gaussian factors and exponential utilities

We analyse the equilibrium asset pricing implications for an economy with single period return exposures to explicit non-Gaussian systematic factors, that may be both skewed and long-tailed, and Gaussian idiosyncratic components. Investors maximize expected exponential utility and equilibrium factor prices are shown to reflect exponentially tilted prices for non-Gaussian factor risk exposures. It is shown that these prices may be directly estimated from the univariate probability law of the factor exposure, given an estimate of average risk aversion in the economy. In addition, a residual form of the capital asset pricing model continues to hold and prices the idiosyncratic or Gaussian risks. The theory is illustrated on data for the US economy using independent components analysis to identify the factors and the variance gamma model to describe the probability law of the non-Gaussian factors. It is shown that the residual CAPM accounts for no more than 1% of the pricing of risky assets, while the exponentially tilted systematic factor risk exposures account for the bulk of risky asset pricing.     

Cross-sectional tests of deterministic volatility functions

We study the cross-sectional performance of option pricing models in which the volatility of the underlying stock is a deterministic function of the stock price and time. For each date in our sample of FTSE 100 index option prices, we fit an implied binomial tree to the panel of all European style options with different strike prices and maturities and then examine how well this model prices a corresponding panel of American style options. We find that the implied binomial tree model performs no better than an ad-hoc procedure of smoothing Black–Scholes implied volatilities across strike prices and maturities. Our cross-sectional results complement the time-series findings of Dumas et al. [J. Finance 53 (1998) 2059].     

Implementing Option Pricing Models When Asset Returns Are Predictable

The predictability of an asset's returns will affect the prices of options on that asset, even though predictability is typically induced by the drift, which does not enter the option pricing formula. For discretely-sampled data, predictability is linked to the parameters that do enter the option pricing formula. We construct an adjustment for predictability to the Black-Scholes formula and show that this adjustment can be important even for small levels of predictability, especially for longer maturity options. We propose several continuous-time linear diffusion processes that can capture broader forms of predictability, and provide numerical examples that illustrate their importance for pricing options.     

Futures Markets and Informational Efficiency: A Laboratory Examination

Through the use of laboratory market methodology, the effect of a futures market on the time path of asset prices is studied and competing models of asset pricing are analyzed. With replication of market conditions, the predictions of a rational expectations equilibrium model are relatively accurate whether or not futures markets are present. However, the presence of futures markets increases the speed with which an efficient equilibrium is achieved. While this more rapid adjustment can increase the variance of spot market prices as they move to equilibrium, this increased variance reflects efficiency gains due to better information.     

Cost-based transfer pricing

This paper compares the performance of alternative cost-based transfer pricing methods. We adopt an incomplete contracting framework with asymmetric information at the trading stage. Transfer pricing guides intra-company trade and provides incentives for value-enhancing specific investments. We compare actual-cost transfer prices that include a markup over marginal costs with standard-cost transfer prices that are determined either by the central office ex ante (centralized standard-cost transfer pricing) or by the supplying division at the trading stage (reported standard-cost transfer pricing). For the actual-cost methods, we show that markups based on the joint contribution margin (contribution-margin transfer pricing) dominate purely additive markups (cost-plus transfer pricing). We obtain the following results. (1) Centralized standard-cost transfer pricing dominates the other methods if the central office and the divisions ex ante face low cost uncertainty. (2) The actual-cost methods dominate the other methods if the central office and the divisions ex ante face high cost uncertainty and later, at the trading stage, the buying division receives sufficient cost information. (3) Reported standard-cost transfer pricing dominates the other methods if the central office and the divisions ex ante face high cost uncertainty, and the buyer has insufficient cost information at the trading stage.     

The Dividend Pricing Model: New Evidence from the Korean Housing Market

It is generally conceded that dividend pricing models are poor predictors of asset prices. This finding is sometimes attributed to excess volatility or to a dividend process manipulated by firm managers. In this paper, we present rather powerful panel tests of the dividend pricing relation using a unique data set in which dividends are set by market forces independent of managers' preferences. We rely on observations on the market for condominium dwellings in Korea—perhaps the only market in which information on dividends and prices is publicly and continuously available to consumers and investors. We extend the “dividend-price ratio model” to panels of housing returns and rents differentiated by type and location. We find broad support for the dividend pricing model during periods both before and after the Asian Financial Crisis of 1997–1998, suggesting that the market for housing assets in Korea has been remarkably efficient. Previous versions of this paper were presented at the Hong Kong-Singapore International Real Estate Research Symposium, August 2004, Hong Kong and the meeting of the Hong Kong Economic Association, January 2005. We are grateful for the comments of Ashok Bardhan, Yuming Fu, Chinmoy Ghosh, Lok Sang Ho, Charles Ka Yui Leung, Sau Kim Lum and Seow Eng Ong. Son's research was supported by the Konkuk University and Hwang's research was supported by the National University of Singapore.     

Convenient prices, currency, and nominal rigidity: Theory with evidence from newspaper prices

Certain items’ prices are often set to simplify and expedite transactions, by coinciding with available monetary units, requiring few pieces of money, or requiring little change. In this sense, these prices are more convenient than other proximate prices. This paper models a firm that explicitly incorporates convenience into its pricing decisions—where convenience is quantified by the number of currency units in a transaction—and illustrates the theoretical behaviors that can arise. Newspaper cover price data empirically support the theory. Across a broader range of goods and services, convenience appears to play a role in effecting above-average nominal price rigidity.     

International capital asset pricing: Evidence from options

We study the risk dynamics and pricing in international economies through a joint analysis of the time-series returns and option prices on three equity indexes underlying three economies: the S&P 500 Index of the United States, the FTSE 100 Index of the United Kingdom, and the Nikkei-225 Stock Average of Japan. We develop an international capital asset pricing model, under which the return on each equity index is decomposed into two orthogonal jump-diffusion components: a global component and a country-specific component. We apply separate stochastic time changes to the two components so that stochastic volatility can come from both global and country-specific risks. For each economy, we assign separate market prices for the two return risk components and the two volatility risk components. Under this specification, we obtain tractable option pricing solutions. Model estimation reveals several interesting insights. First, global and country-specific return and volatility risks show different dynamics. Global return movements contain a larger discontinuous component, and global return volatility is more persistent than the country-specific counterparts. Second, investors charge positive prices for global return risk and negative prices for volatility risk, suggesting that investors are willing to pay positive premiums to hedge against downside global return movements and upside volatility movements. Third, the three economies contain different risk profiles and also price risks differently. Japan contains the largest idiosyncratic risk component and smallest global risk component. Investors in the Japanese market also price more heavily against future volatility increases than against future market downfalls.