The implied volatility surface describes the dependence of options prices on their moneyness (volatility smiles) and maturity characteristics (volatility term structure). This paper presents an empirical study of the factors determining the implied volatility surface for equity options. The first group of factors originates from the features of the stochastic process for the price of the underlying asset. Central to the problem of option valuation is the average quadratic variation, and, more specifically, its continuous and jump components. The evolution of an underlying’s asset price is due to continuous dynamics and jump activity.
In the standard competing auctions model, many sellers compete to sell a single good by offering auctions to buyers. In the first stage of the game sellers post auctions. In the second stage buyers choose one particular auction, place their bid and the good goes to the higest bidder paying the second highest bid. Both the resources available to buyers and the quantity of the good at each auction are exogenously given. In this paper we endogenize both. We first allow buyers to choose the amount of money they bring to an auction, trading off the cost of holding money with the expected surplus from participating in an auction. Second, we allow sellers to choose how much of their production good they want to put on auction, trading off the production cost of the advertised quantity against the expected number of potential buyers. Finally, we allow sellers to charge each buyer with a fee for participating to their auction. This fee, which can be positive or negative, trades off the additional revenue (or cost) from the fee with the number of buyers taking part into their auction. We use our model to study how monetary policy affects the equilibrium allocation of a competing auctions economy and derive recommendations for optimal monetary policy in this environment.
To conduct this exercise we embed the competing auctions framework into the Lagos and Wright (2005) model of monetary exchange with two&sided divisibility. This model is in the tradition of Kiyotaki and Wrightns (1991, 1993) environment in which a role for fiat money is determined endogenously from the frictions of the trading environment, i.e. money is essential for trade (Kocherlakota, 1998; Wallace, 2001). In terms of equilibrium we build on the limit equilibrium concept developed by Peters and Severinov (1997), and extends it to the context of a monetary economy. We build a competing auction environment, start with a finite number of buyers and sellers, characterize the posted contracts, payoffs and money holdings, and then take the limit of these expressions in the infinite game. This limit equilibrium enables to exploit the convergence properties of a competitive matching economy, especially that the deviation by one seller will not affect the payoff buyers can get by visiting him. This corresponds to the market utility property (Peters, 2000) by which the buyerns utility in competitive matching economies is determined by the market and is taken as given by sellers. Finally we assume rational expectations so that sellers believe that their payoff functions satisfy the market utility property.
An entrepreneur owns a business and bears significant risks/rewards from the business. Casual observations and empirical studies have shown that active businesses account for a large fraction of entrepreneurs’ total wealth and that entrepreneurial firms tend to have highly concentrated ownership. Moreover, entrepreneurs often face liquidity constraints. Lack of diversification and liquidity constraints cause business decisions (capital accumulation and entry/exit) and household decisions (consumption/saving and asset allocation) to be highly interdependent. In a recent survey of research, Quadrini (2009) discusses the importance of borrowing constraints and non-diversification on entrepreneurial career choice, entrepreneurial saving/investment, and economic development/growth.
