The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Option-pricing in incomplete markets: the hedging portfolio plus a risk premium-based recursive approach

Consider a non-spanned security $C_{T}$ in an incomplete market. We study the risk/return tradeoffs generated if this security is sold for an arbitrage-free price $\hat{C_{0}}$ and then hedged. We consider recursive "one-period optimal" self-financing hedging strategies, a simple but tractable criterion. For continuous trading, diffusion processes, the one-period minimum variance portfolio is optimal. Let $C_{0}(0)$ be its price. Self-financing implies that the residual risk is equal to the sum of the one-period orthogonal hedging errors, $\sum_{t\leq T} Y_{t}(0) e^{r(T -t)}$. To compensate the residual risk, a risk premium $y_{t}\Delta t$ is associated with every $Y_{t}$. Now let $C_{0}(y)$ be the price of the hedging portfolio, and $\sum_{t\leq T}(Y_{t}(y)+y_{t}\Delta t)e^{r(T-t)}$ is the total residual risk. Although not the same, the one-period hedging errors $Y_{t}(0) and Y_{t}(y)$ are orthogonal to the trading assets, and are perfectly correlated. This implies that the spanned option payoff does not depend on y. Let $\hat{C_{0}}-C_{0}(y)$. A main result follows. Any arbitrage-free price, $\hat{C_{0}}$, is just the price of a hedging portfolio (such as in a complete market), $C_{0}(0)$, plus a premium, $\hat{C_{0}}-C_{0}(0)$. That is, $C_{0}(0)$ is the price of the option's payoff which can be spanned, and $\hat{C_{0}}-C_{0}(0)$ is the premium associated with the option's payoff which cannot be spanned (and yields a contingent risk premium of sum $y_{t}\Delta$t$e^{r(T-t)}$ at maturity). We study other applications of option-pricing theory as well

Mixed-integer second-order cone programming for lower hedging of American contingent claims in incomplete markets

Cataloged from PDF version of article.We describe a challenging class of large mixed-integer second-order cone programming models which arise in computing the maximum price that a buyer is willing to disburse to acquire an American contingent claim in an incomplete financial market with no arbitrage opportunity. Taking the viewpoint of an investor who is willing to allow a controlled amount of risk by replacing the classical no-arbitrage assumption with a "no good-deal assumption" defined using an arbitrage-adjusted Sharpe ratio criterion we formulate the problem of computing the pricing and hedging of an American option in a financial market described by amulti-period, discrete-time, finite-state scenario tree as a large-scale mixed-integer conic optimization problem. We report computational results with off-the-shelf mixed-integer conic optimization software

A Theory of Housing Collateral, Consumption Insurance and Risk Premia

In a model with housing collateral, the ratio of housing wealth to total wealth shifts the conditional distribution of asset prices and consumption growth. A decrease in house prices reduces the collateral value of housing, increases household exposure to idiosyncratic risk, and increases the conditional market price of risk. The model quantitatively accounts for conditional asset pricing moments, cross-sectional variation in value portfolio returns and key unconditional asset pricing moments. The increase of the equity premium and Sharpe ratio when collateral is scarce matches the increase observed in US data. The model also generates a return spread of value firms over growth firms of the magnitude observed in the data. Assets with payoffs that lay farther in the future are less risky. Growth stocks are such long duration assets

Option Pricing Kernels and the ICAPM

We estimate the parameters of pricing kernels that depend on both aggregate wealth and state variables that describe the investment opportunity set, using FTSE 100 and S&P 500 index option returns as the returns to be priced. The coefficients of the state variables are highly significant and remarkably consistent across specifications of the pricing kernel, and across the two markets. The results provide further evidence that, consistent with Merton's (1973) Intertemporal Capital Asset Pricing Model, state variables in addition to market risk are priced

Recovering Probabilities and Risk Aversion from Option Prices and Realized Returns

This paper summarizes a program of research we have conducted over the past four years. So far, it has produced two published articles, one forthcoming paper, one working paper currently under review at a journal, and three working papers in progress. The research concerns the recovery of market-wide risk-neutral probabilities and risk aversion from option prices. The work is built on the idea that risk-neutral probabilities (or their related state-contingent prices) are an amalgam of consensus subjective probabilities and consensus risk aversion. The most significant departure of this work is that it reverses the normal direction of previous research, which typically moves from assumptions governing subjective probabilities and risk aversion, to conclusions about risk-neutral probabilities. Our work is partially motivated by the conspicuous failure of the Black-Scholes formula to explain the prices of index options in the post-1987 crash market. First, we independently estimate risk-neutral probabilities, taking advantage of the now highly liquid index option market. We show that, if the options market is free of general arbitrage opportunities and we can at least initially ignore trading costs, there are quite robust methods for recovering these probabilities. Second, with these probabilities in hand, we use the method of implied binomial trees to recover a consistent stochastic process followed by the underlying asset price. Third, we provide an empirical test of implied trees against alternative option pricing models (including “naïve trader” approaches) by using them to forecast future option smiles. Fourth, we argue that realized historical distributions will be a reliable proxy for certain aspects of the true subjective distributions. We then use these observed aspects together with the option-implied risk-neutral probabilities to estimate market-wide risk aversion.Risk Aversion; Option; Realized Returns

Start-ups Defined as Portfolios of Embedded Options

In this paper we show the advantages of staged investments for venture capitalists. We develop an option-pricing model that enables to evaluate the flexibility acquired by a venture capitalist when he stages his investment process. Instead of investing a fixed amount at the beginning of the investment, the venture capitalist proceeds to a staged investment (one first investment and a second investment). The second investment will be triggered by a successful achievement of the first investment. Should the first investment be unsuccessful, the second investment will not be executed. Staging the investment in two phases enables the investor to reduce its uncertainty at the beginning of the project. As it will be demonstrated in the paper, the decision to proceed to the second investment can be modelled as a portfolio of a call option and a binary option.real options, staged investments, structured products, embedded options

Arbitrage and Control Problems in Finance. Presentation.

The theory of asset pricing takes its roots in the Arrow-Debreu model (see,for instance, Debreu 1959, Chap. 7), the Black and Scholes (1973) formula,and the Cox and Ross (1976) linear pricing model. This theory and its link to arbitrage has been formalized in a general framework by Harrison and Kreps (1979), Harrison and Pliska (1981, 1983), and Du¢e and Huang (1986). In these models, security markets are assumed to be frictionless: securities can be sold short in unlimited amounts, the borrowing and lending rates are equal, and there is no transaction cost. The main result is that the price process of traded securities is arbitrage free if and only if there exists some equivalent probability measure that transforms it into a martingale, when normalized by the numeraire. Contingent claims can then be priced by taking the expected value of their (normalized) payo§ with respect to any equivalent martingale measure. If this value is unique, the claim is said to be priced by arbitrage and it can be perfectly hedged (i.e. duplicated) by dynamic trading. When the markets are dynamically complete, there is only one such a and any contingent claim is priced by arbitrage. The of each state of the world for this probability measure can be interpreted as the state price of the economy (the prices of $1 tomorrow in that state of the world) as well as the marginal utilities (for consumption in that state of the world) of rational agents maximizing their expected utility.arbitrage, control problem

Option-Pricing in Incomplete Markets: The Hedging Portfolio plus a Risk Premium-Based Recursive Approach

Consider a non-spanned security C_{T} in an incomplete market. We study the risk/return trade-offs generated if this security is sold for an arbitrage-free price C₀ and then hedged. We consider recursive "one-period optimal" self-financing hedging strategies, a simple but tractable criterion. For continuous trading, diffusion processes, the one-period minimum variance portfolio is optimal. Let C₀(0) be its price. Self-financing implies that the residual risk is equal to the sum of the one-period orthogonal hedging errors, ∑_{t≤T}Y_{t}(0)e^{r(T-t)}. To compensate the residual risk, a risk premium y_{t}Δt is associated with every Y_{t}. Now let C₀(y) be the price of the hedging portfolio, and ∑_{t≤T}(Y_{t}(y)+y_{t}Δt)e^{r(T-t)} is the total residual risk. Although not the same, the one-period hedging errors Y_{t}(0) and Y_{t}(y) are orthogonal to the trading assets, and are perfectly correlated. This implies that the spanned option payoff does not depend on y. Let C₀=C₀(y). A main result follows. Any arbitrage-free price, C₀, is just the price of a hedging portfolio (such as in a complete market), C₀(0), plus a premium, C₀-C₀(0). That is, C₀(0) is the price of the option's payoff which can be spanned, and C₀-C₀(0) is the premium associated with the option's payoff which cannot be spanned (and yields a contingent risk premium of ∑y_{t}Δte^{r(T-t)} at maturity). We study other applications of option-pricing theory as wellOption Pricing; Incomplete Markets