What are the quantitative finance papers that we should all have in our shelves?

Question

Which quantitative finance papers should we all know about? What are the seminal references in various quantitative finance areas such as empirical asset pricing and theoretical asset pricing?

Answer 1

The following list ranges from the staples to some of the more eclectic titles:

Factor Investing

1. Eugene F. Fama, Kenneth R. French. A five-factor asset pricing model. Journal of Financial Economics, Volume 116, Issue 1, April 2015, Pages 1–22

A five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than the three-factor model of Fama and French (FF, 1993). The five-factor model׳s main problem is its failure to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability. The model׳s performance is not sensitive to the way its factors are defined. With the addition of profitability and investment factors, the value factor of the FF three-factor model becomes redundant for describing average returns in the sample we examine.

2. Campbell R. Harvey, Yan Liu, Heqing Zhu. ...and the Cross-Section of Expected Returns. Oct 2014

Hundreds of papers and factors attempt to explain the cross-section of expected returns. Given this extensive data mining, it does not make sense to use the usual criteria for establishing significance. Which hurdle should be used for current research? Our paper introduces a new multiple testing framework and provides historical cutoffs from the first empirical tests in 1967 to today. A new factor needs to clear a much higher hurdle, with a t-statistic greater than 3.0. We argue that most claimed research findings in financial economics are likely false.

Trading

1. Robert Almgren, Neil Chriss. Optimal Execution of Portfolio Transactions. Dec 2000

We consider the execution of portfolio transactions with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. For a simple linear cost model, we explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty. We may then select optimal strategies either by minimizing a quadratic utility function, or by minimizing Value at Risk. The latter choice leads to the concept of Liquidity-adjusted VAR, or L-VaR, that explicitly considers the best tradeoff between volatility risk and liquidation costs.

2. Charles-Albert Lehalle, Eyal Neuman. Incorporating Signals into Optimal Trading. Apr 2017

Optimal trading is a recent field of research which was initiated by Almgren, Chriss, Bertsimas and Lo in the late 90’s. Its main application is slicing large trading orders, in the interest of minimizing trading costs and potential perturbations of price dynamics due to liquidity shocks. The initial optimization frameworks were based on mean-variance minimization for the trading costs. In the past 15 years, finer modelling of price dynamics, more realistic control variables and different cost functionals were developed. The inclusion of signals (i.e. short term predictors of price dynamics) in optimal trading is a recent development and it is also the subject of this work.

We incorporate a Markovian signal in the optimal trading framework which was initially proposed by Gatheral, Schied, and Slynko [20] and provide results on the existence and uniqueness of an optimal trading strategy. Moreover, we derive an explicit singular optimal strategy for the special case of an OrnsteinUhlenbeck signal and an exponentially decaying transient market impact. The combination of a mean-reverting signal along with a market impact decay is of special interest, since they affect the short term price variations in opposite directions.

Later, we show that in the asymptotic limit were the transient market impact becomes instantaneous, the optimal strategy becomes continuous. This result is compatible with the optimal trading framework which was proposed by Cartea and Jaimungal 5.

Volatility

1. Dennis Yang, Qiang Zhang. Drift‐Independent Volatility Estimation Based on High, Low, Open, and Close Prices The Journal of Business. Vol. 73, No. 3, July 2000, pp. 477-492

We present a new volatility estimator based on multiple periods of high, low, open, and close prices in a historical time series. The new estimator has the following nice properties: it is (a) unbiased in the continuous limit, (b) independent of the drift, (c) consistent in dealing with opening price jumps. Furthermore, it has the smallest variance among all estimators with similar properties. The improvement of accuracy over the classical close-to-close estimator is dramatic for real-life time series.

2. Yacine Aı¨t-Sahalia, Robert Kimmel. Maximum likelihood estimation of stochastic volatility models. Journal of Financial Economics, Vol. 83, 2007, 413–452

We develop and implement a method for maximum likelihood estimation in closed-form of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a shortdated at-the-money option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.

Valuation / Pricing

Of course...

1. Fischer Black, Myron Scholes. The Pricing of Options and Corporate Liabilities. The Journal of Political Econony, Volume 81 Issue 3 (May-Jun 1973), 637-654

If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as a combination of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.

2. Robert C. Merton. Theory of Rational Option Pricing. The Bell Journal of Economics and Management Science. Vol. 4, No. 1 (Spring, 1973), pp. 141-183

The long history of the theory of option pricing began in 1900 when the French mathematician Louis Bachelier deduced an option pricing formula based on the assumption that stock prices follow a Brownian motion with zero drift. Since that time, numerous researchers have contributed to the theory. The present paper begins by deducing a set of restrictions on option pricing formulas from the assumption that investors prefer more to less. These restrictions are necessary conditions for a formula to be consistent with a rational pricing theory. Attention is given to the problems created when dividends are paid on the underlying common stock and when the terms of the option contract can be changed explicitly by a change in exercise price or implicitly by a shift in the investment or capital structure policy of the firm. Since the deduced restrictions are not sufficient to uniquely determine an option pricing formula, additional assumptions are introduced to examine and extend the seminal Black-Scholes theory of option pricing. Explicit formulas for pricing both call and put options as well as for warrants and the new "down-and-out" option are derived. The effects of dividends and call provisions on the warrant price are examined. The possibilities for further extension of the theory to the pricing of corporate liabilities are discussed.

3. J. Michael Harrison, Stanley R. Pliska. "Martingales and stochastic integrals in the theory of continuous trading". Stochastic Processes and their Applications. Volume 11, Issue 3, 1981, pp. 215-260

This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain class, and the general stochastic integral is used to represent capital gains. Within the framework of this model, we discuss the modern theory of contingent claim valuation, including the celebrated option pricing formula of Black and Scholes. It is shown that the security market is complete if and only if its vector price process has a certain martingale representation property. A multidimensional generalization of the Black-Scholes model is examined in some detail, and some other examples are discussed briefly.

4. Hans Gerber, Elias Shiu. Martingale Approach to Pricing Perpetual American Options. International Actuarial Journal. Volume 24, Issue 2 November 1994 , pp. 195-220

The method of Esscher transforms is a tool for valuing options on a stock, if the logarithm of the stock price is governed by a stochastic process with stationary and independent increments. The price of a derivative security is calculated as the expectation, with respect to the risk-neutral Esscher measure, of the discounted payoffs. Applying the optional sampling theorem we derive a simple, yet general formula for the price of a perpetual American put option on a stock whose downward movements are skip-free. Similarly, we obtain a formula for the price of a perpetual American call option on a stock whose upward movements are skip-free. Under the classical assumption that the stock price is a geometric Brownian motion, the general perpetual American contingent claim is analysed, and formulas for the perpetual down-and-out call option and Russian option are obtained. The martingale approach avoids the use of differential equations and provides additional insight. We also explain the relationship between Samuelson's high contact condition and the first order condition for optimality.

5. Hélyette Geman, Nicole El Karoui, Jean-Charles Rochet. "Changes of Numéraire, Changes of Probability Measure and Option Pricing". Journal of Applied Probability. Volume 32, 1995, 443-458

The use of the risk-neutral probability measure has proved to be very powerful for computing the prices of contingent claims in the context of complete markets, or the prices of redundant securities when the assumption of complete markets is relaxed. We show here that many other probability measures can be defined in the same way to solve different asset-pricing problems, in particular option pricing. Moreover, these probability measure changes are in fact associated with numéraire changes; this feature, besides providing a financial interpretation, permits efficient selection of the numéraire appropriate for the pricing of a given contingent claim and also permits exhibition of the hedging portfolio, which is in many respects more important than the valuation itself.

The key theorem of general numéraire change is illustrated by many examples, among which the extension to a stochastic interest rates framework of the Margrabe formula, Geske formula, etc.

Commodities

1. Eduardo Schwartz, James E. Smith. Short-Term Variations and Long-Term Dynamics in Commodity Prices. Management Science © 2000 INFORMS Vol. 46, No. 7, July 2000 pp. 893–911

In this article, we develop a two-factor model of commodity prices that allows mean-reversion in short-term prices and uncertainty in the equilibrium level to which prices revert. Although these two factors are not directly observable, they may be estimated from spot and futures prices. Intuitively, movements in prices for long-maturity futures contracts provide information about the equilibrium price level, and differences between the prices for the short- and long-term contracts provide information about short-term variations in prices. We show that, although this model does not explicitly consider changes in convenience yields over time, this short-term/long-term model is equivalent to the stochastic convenience yield model developed in Gibson and Schwartz (1990). We estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil-linked assets to demonstrate its use and some of its advantages over the Gibson-Schwartz model.

2. Robert S. Pindyck. The Long-Run Evolution of Energy Prices. The Energy Journal. Vol. 20, No. 2 (1999), pp. 1-27

I examine the long-run behavior of oil, coal, and natural gas prices, using up to 127 years of data, and address the following questions: What does over a century of data tell us about the stochastic dynamics of price evolution, and how it should be modeled? Can models of reversion to stochastically fluctuating trend lines help us forecast prices over horizons of 20 years or more? And what do the answers to these questions tell us about investment decisions that are dependent on prices and their stochastic evolution?

3. Eugene F. Fama, Kenneth R. French. Commodity Futures Prices: Some Evidence on Forecast Power, Premiums, and the Theory of Storage. The Journal of Business; Vol. 60, No. 1 (Jan., 1987), pp. 55-73

We examine two models of commodities futures prices. The theory of storage explains the difference between contemporaneous futures and spot prices (the basis) in terms of interest changes, warehousing cost, and convenience yields. We find evidence of variation in the basis in response to both interest rates and seasonal convenience yields. The second model splits a futures price into an expected premium and a forcast of the maturity spot price. We find evidence of forecast power for 10 of 21 commodities and time-varying expected premiums for five commodities.

Answer 2

While no list can be thorough on this subject, I would like to add that an important literature surveys the use and performance of GARCH models, especially with regards to pricing equity options on indexes. The main advantage of using GARCH models here is that the one-step ahead predictability of the underlying conditional variance process greatly facilitates estimation and implementation.

Key references:

1. Duan, J. C. (1995). The GARCH option pricing model. Mathematical Finance, 5(1), 13-32. This is the first paper which provides pricing results using a GARCH model. Duan justifies his risk-neutralization approach based on an equilibrium argument, much like Heston (1993). However, unlike Heston (1993), here you need MC simulations to obtain a price.

2. Heston, S. L., & Nandi, S. (2000). A closed-form GARCH option valuation model. The Review of Financial Studies, 13(3), 585-625. They make a slight modification to the model proposed by Duan (1995) so that the conditional moment generating function of log returns is affine in the conditional variance, so here you can price as in Heston (1993) using the Inverse Fourrier Transform. Later papers call this the affine GARCH because moments are affine in variance.

3. Christoffersen, P., Elkamhi, R., Feunou, B., & Jacobs, K. (2010). Option valuation with conditional heteroskedasticity and nonnormality. The Review of Financial Studies, 23(5), 2139-2183. This paper is important because it casts the pricing problem as a matter of picking (i) a physical process and (ii) a pricing kernel. They give you conditions under which a pricing kernel is valid that do not rely on an equilibrium argument. This is very important because it provides guidelines to explore pricing kernels in a reduced-form setting without having to bother about whether some equilibrium model justifies it.

Personally, I absolutely love that literature. It's really intriguing how something so simple can be extended in so many ways and produce vast detailed discussions about what is going on. It's also somewhat amusing to note that Heston has become an heavy weight contributor in this literature.