The paper proposes an original class of models for the continuous time price process of a financial security with non-constant volatility. The idea is to define instantaneous volatility in terms of exponentially-weighted moments of historic log-price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that unlike many other models of non-constant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference-independent options prices. We find a partial differential equation for the price of a European Call Option. Smiles and skews are found in the resulting plots of implied volatility. Keywords: Option pricing, stochastic volatility, complete markets, smiles. Acknowledgement. It is a pleasure to thank the referees of an earlier draft of this paper whose perceptive comments have resulted in many improvements. 1 Research supported in part by Record Treasu...

The aim of this article is to find bounds on the prices of exotic derivatives, and in particular the lookback option, in terms of the (market) prices of call options. This is achieved without making explicit assumptions about the dynamics of the price process of the underlying asset, but rather by inferring information about the potential distribution of asset prices from the call prices. Thus the bounds we obtain and the associated hedging strategies are model independent. The appeal and significance of the hedging strategies arises from their universality and robustness to model mis-specification. 1 Call Options as Traded Assets Trading in call options is now so liquid that some authors (including Dupire [5, 6]) have argued that calls should no longer be treated as derivative assets to be priced using a Black-Scholes model (or otherwise). Instead calls should be treated as primary assets, whose prices are fixed exogenously by market sentiments. It is only more complicated continge...

This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behaviour of the underlying are in some sense incorporated into the hedge and do not need to be specied exogenously. Thus we are able to nd prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying follows an exponential Brownian motion. We nd model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating prots at zero risk. Examples illustrate that the bounds we give can be fairly tight. 1 Super-replication and robust hedging The focus of this article is an analysis of the hedging of barrier options. The standard...

Partial government guarantees of private financing can be an effective tool for maintaining public-private partnerships. Loan guarantees that cover some or all of the risk of repayment are frequently used by governments to pursue policy objectives–supporting priority infrastructure projects or corporations in financial distress. Studies show that guarantees are extremely valuable–the value of a guarantee increases with the risk of the underlying asset or credit, the size of the investment, and the time to maturity. The flip side of a guarantee’s value to a lender is a cost to the Government. Such a cost is not explicit, but is nevertheless real. To the extent, these liabilities have a subsidy component, careful risk sharing, valuation, and accounting mechanisms are important. This paper describes methods of guarantee valuation, reports estimates of guarantee values in different settings, and summarizes methods of guarantee accounting and their implications. While the old method recorded guarantees only when a default occurred, new methods seek to anticipate losses, create reserves, and channel funds through transparent accounts to ensure that costs of guarantees are evident to decision makers. We describe the federal U.S. Credit Reform Act of 1990 to illustrate accounting trends. Loan guarantees that cover some or all of the risk of debt repayment have, in the past, been

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Prices of riskfree bonds in any arbitrage-free environment are governed by a pricing kernel: given a kernel, we can compute prices of bonds of any maturity we like. We use observed prices of multi-period bonds to estimate, in a log-linear theoretical setting, the pricing kernel that gave rise to them. The high-order dynamics of our estimated kernel help to explain why first-order, one-factor models of the term structure have had difficulty reconciling the shape of the yield curve with the persistence of the short rate. We use the estimated kernel to provide a new perspective on Hansen-Jagannathan bounds, the price of risk, and the pricing of bond options and futures. JEL Classification Codes: E43, G12, G13. Keywords: pricing kernel, price of risk, options, futures. The authors thank Ned Elton, Stephen Figlewski, Silverio Foresi, James MacKinnon, Fallaw Sowell, and Chris Telmer for helpful comments and suggestions. Backus thanks the National Science Foundation for financial support. ...

We approach stock selection for long/short portfolios from the perspective of knowledge discovery in databases and rule induction: given a database of historical information on some universe of stocks, discover rules from the data that will allow one to predict which stocks are likely to have exceptionally high or low returns in the future. Long/short portfolios allow a fund manager to independently address value-added stock selection and factor exposure, and are a popular tool in financial engineering. For stock selection we employed the Recon 1 system, which is able to induce a set of rules to model the data it is given. We evaluate Recon's stock selection performance by using it to build equitized long/short portfolios over eighteen quarters of historical data from October 1988 to March 1993, repeatedly using the previous four quarters of data to build a model which is then used to rank stocks in the current quarter. When trading costs were taken into account, Recon's equitized lo...

This paper examines possible barriers to securitization, focusing on behavioral responses to such novel instruments. These barriers include the difficulties of conveying the associated risks, even to investors who are sophisticated about finance (but still uncertain about model risk and structural uncertainties). Our analyses will draw on results in behavioral decision making and psychology. They will lead to proposals for empirical research and general strategies for making securities design more consonant with investor behavior.

This paper develops a new strategy for dynamically hedging mortgage-backed securities (MBSs).

The object of this paper is to provide a price for options depending on the maximum value of the underlying asset when the contract stipulates that the maximum is taken at discrete times during the life of the option. A general method is provided for the computation of a lower bound to the price using results on the Brownian meander complementing the commonly used upper bound which approximates the discrete maximum by the continuous maximum.. Moreover, in the particular case of the European Put Lookback option, a correction factor associated to the lower bound provides a very good numerical approximation to the price of the option which was otherwise obtained by Monte-Carlo methods. Keywords Brownian Meander, Lookback options, Denisov Decomposition. 1