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

We propose a nonparametric method for estimating derivative financial asset pricing formulae using learning networks. To demonstrate feasibility, we first 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 functions, multilayer perceptrons, and projection pursuit. To illustrate practical relevance, we also apply our approach to S&P 500 futures options data from 1987 to 1991.

Temporary and Permanent Buyout Prices in Online Auctions

Increasingly used in online auctions, buyout prices allow bidders to instantly purchase the item listed. We distinguish two types: a temporary buyout option disappears if a bid above the reserve price is made; a permanent one remains throughout the auction or until it is exercised. In a model featuring time-sensitive bidders with uniform valuations and Poisson arrivals but endogenous bidding times, we focus on finding temporary and permanent buyout prices maximizing the seller's discounted revenue, and examine the relative benefit of using each type of option in various environments. We characterize equilibrium bidder strategies in both cases and then solve the problem of maximizing seller's utility by simulation. Our numerical experiments suggest that buyout options may significantly increase a seller’s revenue. Additionally, while a temporary buyout option promotes early bidding, a permanent option gives an incentive to the bidders to bid late, thus leading to concentrated bids near the end of the auction.