Equilibrium Models for Derivatives Markets with Frictions

This thesis develops equilibrium models, and studies the effects of market frictions on risk-sharing, derivatives pricing, and trading patterns.

In the chapter titled "Imbalance-Based Option Pricing", I develop an equilibrium model of fragmented options markets in which option prices and bid-ask spreads are determined by the nonlinear risk imbalance between dealers and customers. In my model, dealers optimally exploit their market power and charge higher spreads for deep out-of-the-money (OTM) options, leading to an endogenous skew in both prices and spreads. In stark contrast to theories of price pressure in option markets, I show how wealth effects can make customers' net demand for options be negatively correlated with option prices. Under natural conditions, the skewness risk premium is positively correlated with the variance risk premium, consistent with the data.

In the chapter titled "The Demand for Commodity Options", we develop a simple equilibrium model in which commercial hedgers, i.e., producers and consumers, use commodity options and futures to hedge price and quantity risk. We derive an explicit relationship between expected futures returns and the hedgers' demand for out-of-the-money options, and show that the demand for both calls and puts are positively related to expected returns, and the relationship is asymmetric, tilted towards puts. We test and confirm the model predictions empirically using the commitment of traders report from CFTC.

In the chapter titled "Electronic Trading in OTC Markets vs. Centralized Exchange", we model a two-tiered market structure in which an investor can trade an asset on a trading platform with a set of dealers who in turn have access to an interdealer market. The investor's order is informative about the asset's payoff and dealers who were contacted by the investor use this information in the interdealer market. Increasing the number of contacted dealers lowers markups through competition but increases the dealers' costs of providing the asset through information leakage. We then compare a centralized market in which investors can trade among themselves in a central limit order book to a market in which investors have to use the electronic platform to trade the asset. With imperfect competition among dealers, investor welfare is higher in the centralized market if private values are strongly dispersed or if the mass of investors is large.

Three Essays on Asset Pricing

Emmanuel Leclercq

In the first chapter,which is a joint work with Mathieu Cambou and Philippe H.A. Charmoy, we study the distribution of the hedging errors of a European call option for the delta and variance-minimizing strategies. Considering the setting proposed by Heston (1993), we assess the error distribution by computing its moments under the real-world probability measure. It turns out that one is better off implementing either a delta hedging or a variance-minimizing strategy, depending on the strike and maturity of the option under consideration. In the second paper, which is a joint work with Damir Filipovic and Loriano Mancini, we develop a practicable continuous-time dynamic arbitrage-free model for the pricing of European contingent claims. Using the framework introduced by Carmona and Nadtochiy (2011, 2012), the stock price is modeled as a semi-martingale process and, at each time t , the marginal distribution of the European option prices is coded by an auxiliary process that starts at t and follows an exponential additive process. The jump intensity that characterizes these auxiliary processes is then set in motion by means of stochastic dynamics of Itô's type. The model is a modification of the one proposed by Carmona and Nadtochiy, as only finitely many jump sizes are assumed. This crucial assumption implies that the jump intensities are taken values in only a finitedimensional space. In this setup, explicit necessary and sufficient consistency conditions that guarantee the absence of arbitrage are provided. A practicable dynamic model verifying them is proposed and estimated, using options on the S&P 500. Finally, the hedging of variance swap contracts is considered. It is shown that under certain conditions, a variance-minimizing hedging portfolio gives lower hedging errors on average, compared to a model-free hedging strategy. In the third and last chapter, which is a joint work with Rémy Praz, we concentrate on the commodity markets and try to understand the impact of financiers on the hedging decisions. We look at the changes in the spot price, variance, production and hedging choices of both producers and financiers, when the mass of financiers in the economy increases. We develop an equilibrium model of commodity spot and futures markets in which commodity production, consumption, and speculation are endogenously determined. Financiers facilitate hedging by the commodity suppliers. The entry of new financiers thus increases the supply of the commodity and decreases the expected spot prices, to the benefits of the end-users. However, this entry may be detrimental to the producers, as they do not internalize the price reduction due to greater aggregate supply. In the presence of asymmetric information, speculation on the futures market serves as a learning device. The futures price and open interest reveal different pieces of private information regarding the supply and demand side of the spot market, respectively. When the accuracy of private information is low, the entry of new financiers makes both production and spot prices more volatile. The entry of new financiers typically increases the correlation between financial and commodity markets.

EPFL2014

Polynomial models in finance

Damien Edouard Ackerer

This thesis presents new flexible dynamic stochastic models for the evolution of market prices and new methods for the valuation of derivatives. These models and methods build on the recently characterized class of polynomial jump-diffusion processes for which the conditional moments are analytic. The first half of this thesis is concerned with modelling the fluctuations in the volatility of stock prices, and with the valuation of options on the stock. A new stochastic volatility model for which the squared volatility follows a Jacobi process is presented in the first chapter. The stock price volatility is allowed to continuously fluctuate between a lower and an upper bound, and option prices have closed-form series representations when their payoff functions depend on the stock price at finitely many dates. Truncating these series at some finite order entails accurate option price approximations. This method builds on the series expansion of the ratio between the log price density and an auxiliary density, with respect to an orthonormal basis of polynomials in a weighted Lebesgue space. When the payoff functions can be similarly expanded, the method is particularly efficient computationally. In the second chapter, more flexible choices of weighted spaces are studied in order to obtain new series representations for option prices with faster convergence rates. The option price approximation method can then be applied to various stochastic volatility models. The second half of this thesis is concerned with modelling the default times of firms, and with the pricing of credit risk securities. A new class of credit risk models in which the firm default probability is linear in the factors is presented in the third chapter. The prices of defaultable bonds and credit default swaps have explicit linear-rational expressions in the factors. A polynomial model with compact support and bounded default intensities is developed. This property is exploited to approximate credit derivatives prices by interpolating their payoff functions with polynomials. In the fourth chapter, the joint term structure of default probabilities is flexibly modelled using factor copulas. A generic static framework is developed in which the prices of high dimensional and complex credit securities can be efficiently and exactly computed. Dynamic credit risk models with significant default dependence can in turn be constructed by combining polynomial factor copulas and linear credit risk models.

EPFL2017

Pricing interest rate, dividend, and equity risk

Sander Félix M Willems

This thesis studies the valuation and hedging of financial derivatives, which is fundamental for trading and risk-management operations in financial institutions. The three chapters in this thesis deal with derivatives whose payoffs are linked to interest rates, equity prices, and dividend payments. The first chapter introduces a flexible framework based on polynomial jump-diffusions (PJD) to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. Option prices are approximated efficiently using a moment matching technique based on the principle of maximum entropy. An extensive calibration exercise shows that a parsimonious model specification has a good fit with Euribor interest rate swaps and swaptions, Euro Stoxx 50 index dividend futures and dividend options, and Euro Stoxx 50 index options. The second chapter revisits the problem of pricing a continuously sampled arithmetic Asian option in the classical Black-Scholes setting. An identity in law links the integrated stock price to a one-dimensional polynomial diffusion, a particular instance of the PJD encountered in the first chapter. The Asian option price is approximated by a series expansion based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any special functions are involved. The moment indeterminacy of the log-normal distribution introduces an asymptotic bias in the series, however numerical experiments show that the bias can safely be ignored in practice. The last chapter presents a non-parametric method to construct a maximally smooth discount curve from observed market prices of linear interest rate products such as swaps, forward rate agreements, or coupon bonds. The discount curve is given in closed form and only requires basic linear algebra operations. The method is illustrated with several practical examples.

EPFL2019