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23
Spanning and DerivativeSecurity Valuation
, 1999
"... This paper proposes a methodology for the valuation of contingent securities. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans the payoff universe of most, if not all, derivative assets. In one specific application, from the char ..."
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Cited by 57 (5 self)
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This paper proposes a methodology for the valuation of contingent securities. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans the payoff universe of most, if not all, derivative assets. In one specific application, from the characteristic function of the stateprice density, it is possible to analytically price options on any arbitrary transformation of the underlying uncertainty. By differentiating (or translating) the characteristic function, limitless pricing and/or spanning opportunities can be designed. As made lucid via example contingent claims, by exploiting the unifying spanning concept, the valuation approach affords substantial analytical tractability. The strength and versatility of the methodology is inherent when valuing (1) Averageinterest options; (2) Correlation options; and (3) Discretelymonitored knockout options. For each optionlike security, the characteristic function is strikingly simple (although the corresponding density is unmanageable/indeterminate). This article provides the economic foundations for valuing derivative securities.
Contingent Claims and Market Completeness in a Stochastic Volatility Model, Mathematical Finance, 7, No.4, Oct, 399412. 18 the Quantitative Finance Community Team Wilmott Ed. in Chief: Paul Wilmott paul@wilmott.com Editor: Dan Tudball dan@wilmott.com Wil
, 1997
"... In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatil ..."
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Cited by 40 (0 self)
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In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and its volatility variations are correlated. We also relate the ability of a given contingent claim to complete the market to the convexity of its price function in the current asset price. This allows us to state our results for general contingent claims by examining the convexity of their “admissible arbitrage prices.” KEY WORDS: incomplete market, partial differential equations, maximum principle 1.
Equilibrium Forward Curves for Commodities
 Journal of Finance
, 2000
"... We develop an equilibrium model of the term structure of forward prices for storable commodities. As a consequence of a nonnegativity constraint on inventory, the spot commodity has an embedded timing option that is absent in forward contracts. This option’s value changes over time due to both endog ..."
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Cited by 40 (2 self)
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We develop an equilibrium model of the term structure of forward prices for storable commodities. As a consequence of a nonnegativity constraint on inventory, the spot commodity has an embedded timing option that is absent in forward contracts. This option’s value changes over time due to both endogenous inventory and exogenous transitory shocks to supply and demand. Our model makes predictions about volatilities of forward prices at different horizons and shows how conditional violations of the “Samuelson effect ” occur. We extend the model to incorporate a permanent second factor and calibrate the model to crude oil futures data. COMMODITY MARKETS IN RECENT YEARS have experienced dramatic growth in trading volume, the variety of contracts, and the range of underlying commodities. Market participants are also increasingly sophisticated about recognizing and exercising operational contingencies embedded in delivery contracts. 1 For all of these reasons, there is a widespread interest in models for pricing and hedging commoditylinked contingent claims. In this paper we present an equilibrium model of commodity spot and forward prices. By explicitly incorporating the microeconomics of supply, demand, and storage, our model captures some fundamental differences between commodities and financial assets. Empirically, commodities are strikingly different from stocks, bonds and other conventional financial assets. Among these differences are:
On The Relation Between Option and Stock Prices: A Convex Optimization Approach
, 2000
"... The idea of investigating the relation of option and stock prices just based on the noarbitrage assumption, but without assuming any model for the underlying price dynamics has a long history in the financial economics literature. We introduce convex, and in particular semidefinite, optimization met ..."
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Cited by 39 (9 self)
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The idea of investigating the relation of option and stock prices just based on the noarbitrage assumption, but without assuming any model for the underlying price dynamics has a long history in the financial economics literature. We introduce convex, and in particular semidefinite, optimization methods, duality and complexity theory to shed new light to this relation. For the single stock problem, given moments of the prices of the underlying assets, we show that we can find best possible bounds on option prices with general payoff functions efficiently, either algorithmically (solving a semidefinite optimization problem) or in closed form. Conversely, given observable option prices, we provide best possible bounds on moments of the prices of the underlying assets, as well as on the prices of other options on the same asset by solving linear optimization problems. For options that are affected by multiple stocks either directly (the payoff of the option depends on multiple stocks) or indirectly (we have information on correlations between stock prices), we find nonoptimal bounds using convex optimization methods. However, we show that it is NPhard to find best possible bounds in multiple dimensions. We extend our results to incorporate transactions costs.
If You’re So Smart, Why Aren’t You Rich? Belief Selection in Complete and Incomplete Markets
, 2001
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Dynamic Derivative Strategies
, 2003
"... We study optimal investment strategies given investor access not only to bond and stock markets but also to the derivatives market. The problem is solved in closed form. Derivatives extend the risk and return tradeoffs associated with stochastic volatility and price jumps. As a means of exposure to ..."
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Cited by 33 (5 self)
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We study optimal investment strategies given investor access not only to bond and stock markets but also to the derivatives market. The problem is solved in closed form. Derivatives extend the risk and return tradeoffs associated with stochastic volatility and price jumps. As a means of exposure to volatility risk, derivatives enable nonmyopic investors to exploit the timevarying opportunity set; and as a means of exposure to jump risk, they enable investors to disentangle the simultaneous exposure to diffusive and jump risks in the stock market. Calibrating to the S&P 500 index and options markets, we find sizable portfolio improvement from derivatives investing.
Capital market equilibrium with moral hazard
, 2002
"... This paper studies a general equilibrium model of an economy with production under uncertainty in which firms’ capital (ownership) structures creates a moral hazard problem for their managers. The concept of an equilibrium with rational, competitive price perceptions (RCPP) is introduced, in which i ..."
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Cited by 10 (0 self)
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This paper studies a general equilibrium model of an economy with production under uncertainty in which firms’ capital (ownership) structures creates a moral hazard problem for their managers. The concept of an equilibrium with rational, competitive price perceptions (RCPP) is introduced, in which investors correctly anticipate the optimal effort of entrepreneurs by observing their financial decisions, and entrepreneurs are aware that investors use their financial decisions as signals. The competitive element in the equilibrium valuation of firms comes from the fact that entrepreneurs cannot affect the market price of risks. It is shown that under appropriate spanning assumptions an RCPP is constrained Pareto optimal. Furthermore, if sufficiently many options are traded, then full optimality can be obtained despite the moral hazard problem: options serve both to increase the span of the market and to provide incentives for entrepreneurs.
Operational flexibility and financial hedging: Complements or substitutes
 Management Science
, 2010
"... doi 10.1287/mnsc.1090.1137 ..."
Statistical arbitrage and securities prices
 Review of Financial Studies
, 2003
"... This article introduces the concept of a statistical arbitrage opportunity (SAO). In a finitehorizon economy, a SAO is a zerocost trading strategy for which (i) the expected payoff is positive, and (ii) the conditional expected payoff in each final state of the economy is nonnegative. Unlike a pur ..."
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Cited by 5 (0 self)
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This article introduces the concept of a statistical arbitrage opportunity (SAO). In a finitehorizon economy, a SAO is a zerocost trading strategy for which (i) the expected payoff is positive, and (ii) the conditional expected payoff in each final state of the economy is nonnegative. Unlike a pure arbitrage opportunity, a SAO can have negative payoffs provided that the average payoff in each final state is nonnegative. If the pricing kernel in the economy is path independent, then no SAOs can exist. Furthermore, ruling out SAOs imposes a novel martingaletype restriction on the dynamics of securities prices. The important properties of the restriction are that it (1) is modelfree, in the sense that it requires no parametric assumptions about the true equilibrium model, (2) can be tested in samples affected by selection biases, such as the peso problem, and (3) continues to hold when investors ' beliefs are mistaken. The article argues that one can use the new restriction to empirically resolve the joint hypothesis problem present in the traditional tests of the efficient market hypothesis. In a fairly general environment, this article proposes a novel martingaletype restriction on the dynamics of securities prices. This restriction has a
The Impact Of Energy Derivatives On The Crude Oil Market
, 1999
"... We examine the effects of energy derivatives trading on the crude oil market. There is a common public and regulatory perception that derivative securities increase volatility and can have a destabilizing effect on the underlying market. Consistent with this view, we find an abnormal increase in vol ..."
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Cited by 5 (0 self)
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We examine the effects of energy derivatives trading on the crude oil market. There is a common public and regulatory perception that derivative securities increase volatility and can have a destabilizing effect on the underlying market. Consistent with this view, we find an abnormal increase in volatility for three consecutive weeks following the introduction of NYMEX crude oil futures. While there is also evidence of a longerterm volatility increase, this is likely due to exogenous factors such as the continuing deregulation of the energy markets. Subsequent introductions of crude oil options and derivatives on other energy commodities have no effect on crude oil volatility. We also examine the effects of derivatives trading on the depth and liquidity of the crude oil market. This analysis reveals a strong inverse relation between the open interest in crude oil futures and spot market volatility. Specifically, when open interest is greater, the volatility shock associated with a giv...