Option Pricing Bounds: Synthesis And Extension

The main option pricing bounds in the literature were originally obtained through various disparate methods. I show that those bounds can be derived from a single analytical framework. The key to this synthesis lies in the use of a general expression for the price of a call option depending on the corresponding put option's discount factor. Although the put's discount factor is unknown, it can be bounded from below. I use this lower bound on the put's discount factor to derive traditional lower bounds for call prices. In addition, I extend the literature by finding a new tighter lower bound.     

WHO ARE THE NOISE TRADERS?

Closed‐end funds often trade at a discount to net asset value. Previous research suggests that the positive correlation in discounts is associated with investor sentiment that causes systematic mispricing by noise traders. We use a newly available sample of daily fund valuations to examine the relation between intraday trading activity and discount changes. Contrary to the assumption that retail investors are noise traders, we find no relation between discount changes and the order‐flow imbalances of individual investors. Large daily discount changes are associated with institutional trading, and this may reflect the price inelasticity of closed‐end fund shares.     

The impact of conglomeration on the option value of equity

Using contingent claims analysis, I quantify the effect of risk-reducing corporate diversification on the value of equity as a call option on firm assets. The impact of conglomeration on firm risk is heavily conditioned on firm size. In contrast to small firms, the risk of large firms does not decline with increasing conglomeration. Accounting for this effect, the expected equity discount is much lower than commonly assumed and can even turn into a premium if the path dependency of equity is incorporated. My results stand in direct contrast to those of Mansi and Reeb (2002) and caution against using asset substitution as a qualitative argument for explaining economy-wide value phenomena.     

Cashflow news,the value premium and an asset pricing view on European stock market integration

The decomposition of national CAPM market betas of European countries’ value and growth portfolio returns into cashflow and discount rate news driven components reveals that i) high average returns on value portfolios are associated with disproportionately high sensitivity to national cashflow news which corroborates recent evidence for the U.S. and ii) two-beta variants of national CAPMs capture the cross-sectional dispersion in European stock returns. The latter finding is suggestive of relatively well integrated stock markets among the core European countries and reflects basic asset pricing theory. One (national) discount factor should price any (international) asset.     

Valuing and pricing IPOs

This paper investigates how underwriters set the IPO firm’s fair value, an ex-ante estimate of the market value, using a unique dataset of 228 reports from French underwriters. These reports are issued before the IPO shares start trading on the stock market and detail how underwriters determined fair value. We document that underwriters often employ multiples valuation, dividend discount models and discounted cash flow (DCF) analysis to determine fair value but that all of these valuation methods suffer from a positive bias with respect to equilibrium market value. We also analyze how this fair value estimate is subsequently used as a basis for IPO pricing. We report that underwriters deliberately discount the fair value estimate when setting the preliminary offer price. Part of the intentional price discount can be recovered by higher price updates. We find that, controlling for other factors such as investor demand, part of underpricing stems from this intentional price discount.     

Expected Time Value Decay of Options: Implications for Put‐Rolling Strategies

Assuming the underlying asset price remains constant, previous studies show that the time value of an option decays gradually at a rate that accelerates over time and peaks at the expiration date. Thus, a significant portion of time value is lost in the four weeks leading up to expiration. This paper shows the time value of currently at‐ or near‐the‐money options should be expected to decay at a rate that decreases over time. The time values of options that are currently deep‐in‐ or deep‐out‐of‐the‐money are expected to initially rise and then resume the normal decay pattern.     

Exchange Rates and the Conversion of Currency‐Specific Risk Premia

How do the risk factors that drive asset prices influence exchange rates? Are the parameters of asset price processes relevant for specifying exchange rate processes? Most international asset pricing models focus on the analysis of asset returns given exchange rate processes. Little work has been done on the analysis of exchange rates dependent on asset returns. This paper uses an international stochastic discount factor (SDF) framework to analyse the interplay between asset prices and exchange rates. So far, this approach has only been implemented in international term structure models. We find that exchange rates serve to convert currency‐specific discount factors and currency‐specific prices of risk – a result linked to the international arbitrage pricing theory (IAPT). Our empirical investigation of exchange rates and stock markets of four countries presents evidence for the conversion of currency‐specific risk premia by exchange rates.     

Collateralizing liquidity

I develop a dynamic model of optimal funding to understand why financial assets are used as collateral instead of being sold to raise funds. Firms need funds to invest in risky projects with nonobservable returns. Since holding these assets allows firms to raise these funds, investing firms value the asset more than noninvesting ones. When assets are less than perfectly liquid and investment opportunities are persistent, collateralized debt minimizes asset transfers from investing to noninvesting firms and thus is optimal. Frictions in asset markets lead to an illiquidity discount and a collateral premium, which increase with the asset’s illiquidity.     

Valuation of asset leasing contracts

This paper describes the relation among a variety of asset leasing contracts, including: (1) cancellable operating leases; (2) leases which grant the lesse an option to extend the life of the lease; (3) leases that grant the lessee an option to purchase the leased asset at a fixed price at the maturity date of the lease; (4) leases that grant the lessee the right to purchase the leased asset at its ‘fair market value’ at the maturity date of the lease; (5) leases that grant an option to the lessee to purchase the leased asset at a prespecified price anytime during the life of the lease; (6) leases that require the lessee to purchase the leased asset at a fixed price at the maturity date of the lease; and (7) leases that contain non-cancellation provisions. The paper uses a compound option pricing framework to develop a general model for valuing (or evaluating) each of the types of leasing contracts. Numerical examples are presented to illustrate the effect of the various elements of a leasing contract — including cancellation risk and residual value risk — on equilibrium rental payments.     

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

Discounting cash flows requires an equilibrium model to determine the cost of capital. The CAPM of Sharpe and the intertemporal asset pricing model of Merton (1973) offer a theoretical justification for discounting at a constant risk adjusted rate. Two problems arise with this application. First, for mean reverting cash flows the risk adjustment is unknown, and second, if the present value is compounded forward then the distribution of future wealth is likely right skewed. I develop equilibrium discount rates for cash flows whose level or growth rate is mean reverting. Serial correlation also largely eliminates the skewness problem.     

Higher Order Expectations in Asset Pricing

We examine formally Keynes' idea that higher order beliefs can drive a wedge between an asset price and its fundamental value based on expected future payoffs. We call this the higher order wedge, which depends on the difference between higher and first order expectations of future payoffs. We analyze the determinants of this wedge and its impact on the equilibrium price in the context of a dynamic noisy rational expectations model. We show that the wedge reduces asset price volatility and disconnects the price from the present value of future payoffs. The impact of the higher order wedge on the equilibrium price can be quantitatively large.     

American GARCH employee stock option valuation

We implement a flexible simulation-based approach for the fair value of employee stock option (ESO) that accounts for the vesting period, departure risk and voluntary suboptimal early exercise. We introduce GARCH effects on the underlying asset and we analyze the price bias with respect to the constant volatility case. We also perform a sensitivity analysis with respect to changes in several ESO characteristics. We compare this valuation with FAS 123 method revealing a FAS overvaluation. Finally, we value a real ESO plan providing the confidence intervals for the estimated ESO prices.     

SUBORDINATED BINOMIAL OPTION PRICING

We extend the binomial option pricing model to allow for more accurate price dynamics while retaining computational simplicity. The asset price in each binomial period evolves according to two independent and successive Bernoulli trials on trade occurrence/nonoccurrence and up/down price movement. Subordination leads to a trinomial tree with stochastic volatility in calendar time. We derive utility‐dependent valuation results incorporating the leverage effect and test the model empirically.     

Does firm value move too much to be justified by subsequent changes in cash flow?

The appropriate measure of cash flow for valuing corporate assets is net payout, which is the sum of dividends, interest, and net repurchases of equity and debt. Variation in net payout yield, the ratio of net payout to asset value, is mostly driven by movements in expected cash flow growth, instead of movements in discount rates. Net payout yield is less persistent than dividend yield and implies much smaller variation in long-horizon discount rates. Therefore, movements in the value of corporate assets can be justified by changes in expected future cash flow.     

Pitfalls in VAR based return decompositions: A clarification

We analyze the pitfalls involved in VAR based return decompositions. First, we show that recent criticism of such decompositions is misplaced and builds on invalid VAR models and erroneous interpretations. Second, we derive the requirements needed for VAR decompositions to be valid. A crucial – but often neglected – requirement is that the asset price needs to be included as a state variable in the VAR. In equity return decompositions this requirement is equivalent to including the dividend–price ratio in the VAR. Finally, we clarify the intriguing issue of the role of the residual component in return decompositions. In a properly specified first-order VAR, it makes no difference whether cash flow news or discount rate news is backed out residually, and it makes no difference whether both news components are computed directly or one of them is backed out residually.     

Do the equity holding and soundness of bank underwriters affect issue costs of SEOs?

This paper examines the effects of characteristics of bank underwriters on issue costs in seasoned equity offerings in Japan following deregulation in 1999. I find that banks’ holding loans have a negative effect on price discounts and no effect on underwriting fees. However, banks’ equity holdings have no effect on discount rates and a positive effect on underwriting fees. Furthermore, issuers with unhealthy banks pay higher discount rates, are more likely to be weak in their ex-post operating performance, and are less willing to switch underwriters. I conclude that the characteristics of banks have different effects on issue costs.     

Presidential Address: Discount Rates

Discount‐rate variation is the central organizing question of current asset‐pricing research. I survey facts, theories, and applications. Previously, we thought returns were unpredictable, with variation in price‐dividend ratios due to variation in expected cashflows. Now it seems all price‐dividend variation corresponds to discount‐rate variation. We also thought that the cross‐section of expected returns came from the CAPM. Now we have a zoo of new factors. I categorize discount‐rate theories based on central ingredients and data sources. Incorporating discount‐rate variation affects finance applications, including portfolio theory, accounting, cost of capital, capital structure, compensation, and macroeconomics.     

Pricing options on scenario trees

We examine valuation procedures that can be applied to incorporate options in scenario-based portfolio optimization models. Stochastic programming models use discrete scenarios to represent the stochastic evolution of asset prices. At issue is the adoption of suitable procedures to price options on the basis of the postulated discrete distributions of asset prices so as to ensure internally consistent portfolio optimization models. We adapt and implement two methods to price European options in accordance with discrete distributions represented by scenario trees and assess their performance with numerical tests. We consider features of option prices that are observed in practice. We find that asymmetries and/or leptokurtic features in the distribution of the underlying materially affect option prices; we quantify the impact of higher moments (skewness and excess kurtosis) on option prices. We demonstrate through empirical tests using market prices of the S&P500 stock index and options on the index that the proposed procedures consistently approximate the observed prices of options under different market regimes, especially for deep out-of-the-money options.     

The coskewness puzzle

We propose a novel approach to testing non-linear stochastic discount factor (SDF) specifications that arise in rational representative investor models. Our approach does not require overly-restrictive assumptions about the shape of investors’ preferences, typically imposed by the extant literature, and is based instead on restrictions that rule out “good deals”, i.e., arbitrage opportunities as well as unduly large Sharpe ratios. We apply this framework to test the empirical admissibility of 3 and 4-moment versions of the CAPM. We find that, while coskewness and cokurtosis risk help price a number of stock strategies and portfolios, including static strategies based on a fine industry-level diversification, momentum strategies and portfolios managed on the basis of available information, the CAPM and its 3 and 4-moment versions cannot provide an exhaustive account of observed asset returns.     

A computational study on general equilibrium pricing of derivative securities

This paper analyses the accuracy of replicating portfolio methods in predicting asset prices. In a two-period, general equilibrium model with incomplete financial markets and heterogeneous agents, a computational study is conducted under various distributional assumptions. The focus is on the price of a call option on an underlying risky asset. There is evidence that the value of the (approximate) replicating portfolio is a good approximation for the general equilibrium price for CRRA preferences, but not for CARA preferences. Furthermore, there is strong evidence that the introduction of the call option reduces market incompleteness, but that the price of the underlying asset is unchanged. There is, however, inconclusive evidence on the welfare effects of the option. The author thanks Dolf Talman, Andrew Somerville, an anonymous referee, and an Associate Editor for helpful comments. Research funding from the Irish Research Council for the Humanities and Social Sciences is gratefully acknowledged.