A simple nonparametric approach to derivative security valuation

Article Abstract:

'Canonical valuation' uses historical time series to predict the probability distribution of the discounted value of primary assets' discounted prices plus accumulated dividends at any future date. Then the axiomatically-rationalized 'maximum entropy principle' is used to estimate risk-neutral (equivalent martingale) probabilities that correctly price to the primary assets, as well as any predesignated subset of derivative securities whose payoffs occur at this date. Valuation of other derivative securities proceeds by calculation of its discounted, risk-neutral expected value. Both simulation and empirical evidence suggest that canonical valuation has merit. (Reprinted by permission of the publisher.)

Research, Derivatives (Financial instruments), Valuation, Discount rates

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Nonparametric estimation of state-price densities implicit in financial asset prices

Article Abstract:

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. (Reprinted by permission of the publisher.)

Models, Usage, Options (Finance), Pricing, Finance, Nonparametric statistics

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A nonparametric model of term structure dynamics and the market price of interest rate risk

Article Abstract:

This article presents a technique for nonparametrically estimating continuous-time diffusion processes that are observed at discrete intervals. We illustrate the methodology by using daily three and six month Treasury Bill data, from January 1965 to July 1995, to estimate the drift and diffusion of the short rate, and the market price of interest risk. While the estimated diffusion is similar to that estimated by Chan, Karolyi, Longstaff, and Sanders (1992), there is evidence of substantial non-linearity in the drift. This is close to zero for low and medium interest rates, but mean reversion increases sharply at higher interest rates. (Reprinted by permission of the publisher.)

Analysis, Risk (Economics), Interest rates

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